DevoWorm Lab Meetings, 6 Jun 2023

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From YouTube: DevoWorm (2023, Meeting #21): GSoC Updates, R-D Morphogenesis, Particle Lenia, Game of Life and CAs

Description

GSoC Updates. Reaction-Diffusion Morphogenesis in 2-D and 3-D (Turing and Gray-Scott Models). Nonlinear oscillators and B-Z reactions. Connecting PDEs to C-RNNs, Cellular Automata to Reinforcement Learning. Game of Life and Particle Lenia -- Hamiltonian and Continuous representations. Attendees: Sushmanth Reddy Mereddy, Morgan Hough, Susan Crawford-Young, Himanshu Chougule, Bradly Alicea, and Richard Gordon.

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A

Hi, how are you okay, Jesse says: he's double booked? Well, let's, let's go ahead and listen. It's fine.

B

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Has two ears yeah.

A

B

How was everyone today.

B

Okay, tomorrow, tomorrow, I've got.

A

A cataract, yeah yeah, good luck, okay, yeah. What good luck and I'm up late today so I'm, not gonna, see me yeah.

C

I couldn't attend the meeting through my laptop.

C

Update on my past week, work yeah.

C

This week, as coding began, I started working on what I'm saying model I was using the segmented moral slot by torch Library, as minec used for Segment anything integrating with segment anything but the segment anything with an initial phase. There are a lot of Works in their library, and the model was not learning at all. So I tried to use that Library only I fix it, some bugs, but that's not.

C

There are a lot of bugs I couldn't solve so I thought of not using that library and I want to do my whatever fine-tuning the model in a classical methods. So I will be starting. Last week. I have done that. Only solving the bug say: I was trying out error and trial, whether it works or not, but it is not at all working for the small modems. Also so I started using capital.

C

Also after that, next nine weeks, I will completely focus on the owner, as the data set was ready and uh everything is ready. uh I was using sorry I was using a cell tracking challenge data set uh to find the devonet model. It's absolutely fine because it has the ground truth. Images and the pigmented images and the dot images representing the wearable position is that that it would be a perfect data set to Prime that model, so I have already coded the model, but I just need to turn it on so I'll be next.

C

After these two weeks, next nine weeks, I will completely working on that and write a paper on it like how to use it completely like the whole and I have to write unit tests. Also, so I will start working from the this week itself. I will give you update in next week. Actually I wrote a Blog about my community bonding period. Also I hosted it in my website.

C

um I have shared it everywhere and that's what it is every week, I will write a blog week, one week on by tomorrow evening. I will host it and I will give you in the development. Channel and I was pushing them into devoland blocks. Also, so everyone could read it.

A

Oh that's great yeah! Thank you for that.

C

um It's kind of sudden it happened. I was like so from next week. I will be bit prepared and attend meetings in perfectly.

A

Okay, yeah, it's fine! Well, thank you for the update. I did get your message in the slack channel, so I did book that over and then I saw that you had a post. So why don't we look at that now? I'll put it up, ah let's see here we go and so yeah. This is a special month blog. uh He says he's putting this up at Devo, uh Devo, worm or Diva learn the the blog that um it created uh before the community period as well.

A

So uh you can go from the beaverworm.github.io site and you can find it through there. So this is his post on community bonding.

A

uh This is, uh and it talks about you know getting selected for g-soc and uh you know working on the project uh I'm talking about C, elegans data, capturing folder format and files, meaning a data set data analysis, which is this part, uh yeah, instant segmentation and continuing week's comp commitments. So this is just kind of like laying out the next steps. So that looks pretty good.

A

um Let's see that okay yeah.

C

Try to write it more I wrote them very small, like I was thinking to write, commented code in the blog itself, explaining what all code is doing exactly.

C

But I just need to make small updates, but it explains the code. Yes,.

C

In the future, also, they can understand what it's and how it is working and.

A

Yeah I mean that's something you can do like in the code too I mean you know like you can set up a notebook where you can explain some of that, uh but yeah I, don't know how you put it in the in the blog body. I guess you could just take screenshots or there may be some interactive thing. I wouldn't spend gobs of time on it, but you know to see what we can put together. You know you can put together pretty quickly so.

C

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And then this is the repository, so yeah looks like we're: um yeah got the notebooks.

C

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Maybe by to keep it.

A

Very okay: oh okay,.

C

I have told you the line itself right. Sorry.

C

Okay, anyways, that's all my week. Updates I will definitely keep the more books on the board so I'm promising you, this won't repeat next week. I will be updating whole thing by.

A

Sounds good yeah. Thank you. That's.

D

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um Yes, I, look forward to it and uh yeah. Were you uh one more thing you mentioned in the slack that you're going to meet with my yoke this weekend? Did you get to meet with him or.

C

Mike was pretty busy this weekend, so it's not like tomorrow.

C

's classical method s using some libraries to segments, that's what his suggestion is. After his suggestion, only I started working on classical methods of implementing this code. So maybe maybe we'll have a meeting tomorrow and we will discuss it and we will keep that update in the slack Channel.

A

Sounds good yeah, yeah, okay,.

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Thanks and look forward to seeing next week's work and yeah beloved Manchu, how are you.

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uh It's very low.

D

Oh yeah hi how.

A

Are you there, you go.

D

um And give you an update.

A

Yeah, let me answer your mine. First, okay, go ahead.

D

There you go, oh, is everybody? Yes,.

A

Yes, I can see it.

D

uh Okay, uh so uh I basically I've been maintaining one note which has like all the important stuff in it uh compared to like last year, which I did just one document.

D

It was really hard to uh get around things so basically uh for the communicate Community period I've been looking at all the previous year, projects which have been uh similar to uh this year's, uh like the jigs of 2017, 2018, 29 and uh 2019 onwards, and I've been writing some notes about it, like the 2017 project was based on uh like uh classical methods, as uh sushman said right now, and uh it is also something I've been working on uh and then the 2018 uh G-Shock was uh like the continuation of 2017, but it had like some visualizations of the developmental cycles of C elegans and in 2019 there was an unsupervised approach of segmentation uh proposed and then in 2020 onwards it was deep learning days uh so, like I, looked around all the previous uh projects and uh tried to get some influence out of it.

D

uh Also I've been doing some research on uh like the problem statement itself, especially the first part of the problem set, that is to like refactor the segmentation code and uh Thomas a really interesting paper uh on the data set we have used. So this is like the cell tracking overview paper like it's, basically a benchmark of all the 10 years. uh The cell tracking challenge has been held and it was recently accepted uh on 13th April and it was published online on 18..

D

So it's it's really new and in this I I went through the paper and I highlighted all the key points in which, like the C elegans has been uh like. The data set which we are using, uh which has like piff files, has been uh like okay points that have come across regarding that data set. uh So like uh the cell and.

D

uh Basically, uh this uh this diagram over here tells us, although uh techniques and strategies they are, the teams have used which were in this challenge.

D

So uh if you look, uh if you look at over here closely like if unit is something which uh I wanted to do for segmentation and uh as you can see like, around 23 people have uh 23, teams have done unit and, uh and so on, like so it's basically uh across all the teams like how they have proposed this challenge, and so uh as this is the data set, you are using like fluoro and 3D H or CE like fluorescence, and it's a 3D data set and it's of C Elegance.

D

So that's the naming, conjunction I, think and also the this also has, like all the properties like cross segment to noise ratio. Contrast ratio of all the data set which was already given like, uh and this fluoro 2D and simplest, is what we used in stage. One of the table graph Yeah, so basically I, read through this paper and uh some of the inferences I came across was like what type of methods are better for uh which uh data set and uh like an approach to generalize the model.

D

So that it works on most cell tracking uh tasks like segmentation tracking tasks, so one of the main key highlights of this paper was that when we watch all the data sets like uh the C Elegance data set, it does not perform really well, as opposed to other data sets, and the reason behind it is that uh the data set itself is like a 3D data set and it has almost spherical objects and, uh and it has significantly higher descent density. So what we come across as that uh uh this this may.

D

This is the main reason that leads to like uh that. The model is not optimized for this particular data set. Also, uh one key highlight that I wanted to show was uh this like the use of a gaussian bandpass filter for noise removal, so uh like a band pass, filter is like.

D

Basically, uh we convert an image to a signal, and then we do processing on it, like uh that's the conventional way to redo this, and this was a kind of an interesting approach like they use the vitabi algorithm, which is like a hidden Markov model algorithm to I. Do the cell tracking and this lightweight or segmentation, was like really good, so this is one thing I'm like uh looking and so.

D

Okay also, they had like the some some of the codes was, was shared on this GitHub link like cell tracking challenge uh this one, and they had like some Fiji plugins and for all the sources that they are used. Yeah uh also like there are some other papers that I have been reading like this 3D convolutional neural net base segmentation, one which like or which also you see, elegance and also similar to our data set and uh also the topological data analysis, one uh which was the main paper that you had given all for.

D

uh Topological data analysis right yeah. uh So this is the.

D

Like the theory part and then I've been also uh getting my hand into the actual code, so uh right now, I've just defined a new function like which basically uh doesn't use some extended I, really like simple IDK uh to like uh directly load the images into the bytos tensor, which we basically use further in training and developing the model. So the previous method, which has proposed in previous years, was to use a different library, and then you have to read the image in that library and then get an array.

D

Instead of that, we can just use a the ifs file uh CSS file package, which is also like the loaded in collab itself, and then we can just directly load the tensor and it saves a lot of time because we are calling our display images function, a lot of time so basically using this uh I'm using Google, collab and then I.

D

uh Basically, the tff I basically displayed the images, and uh the main thing is like the tsf file is uh into Club select clustered into 35 different chunks, so, like each uh chunk, just tells us a different time step like how the cells are uh in 3D, so 1 to 35 like that. Okay, so this is at zero. uh The first image is at time, step 0 and uh at t 0, and the last image is as t34 this one.

D

So you get like a 3D view from top to bottom exactly, and this is the ground for of the as well like all as well, and then this is uh basically to see if like, which is a better compression uh like PNG, does a less compression loss compared to J5 and uh right now, I'm trying to do the features extraction Parts like uh using a tiny image and Edge your filter, like Edge I've, defined two functions over here, and what I'm trying to do is like to use a thresholding which is like use, uh erogen dilation, and then you uh do the morphology, but it's giving error and like I'm trying I was basically doing that right.

D

Now, uh it's just a shape error that I'll figure out, but this was the update for so.

A

Okay, yeah, that's great! uh So what? What are your plans for next or this week? And you know the coming week.

D

uh So this week, uh I've also been researching on those like the unit. One and there's also a deep and uh deep lab D3 kind of model, which is also there on Torch vision, uh so like I've, been I, was doing some tutorials as well.

D

uh So right now, I'm, just figuring out uh two two parts of it like a model for Segment uh semantic segmentation and a model for image segmentation and uh including both of those and try to do both of uh try to do one of them at a time and then uh train it on solar board.

D

Whichever is uh better for uh depending on the G constraints of data, and so that uh I'll start giving up I'll give the update on slack and also write a blog on the community bonding period as well as the uh coding period starts like I started. I was working on that, but, like it's, not it's still not ready. Yet so. I'll show that.

A

That's true yeah. That sounds great uh yeah. Thank you for that uh yeah you mentioned using models for semantic and image segmentation and I. Don't know if you're aware of such month has been working on uh that.

C

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Thing for evil learned like yeah yeah, so.

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Go ahead: hello, yeah, yeah,.

C

I mean it's perfectly fine, because you measure it to the kind of great files which they have used. It is absolutely primed on Wealthy, well perfected data, and it was fine-tuned again. So if we count to the if I think it couldn't cross the.

C

uh Rather than using a deep lab or something like that, see some new models, actually there are some Twitter in modern schema. Last couple of months right now, I choose segment anything model, uh which is perfectly fine like that you can see other morons which could that point because B flat, maybe it couldn't give you the best results as compared to imagenet, which my you can mine accused. So that's yeah. You can't get the loss value below then my 10 minus, if you use a d prop.

C

This is what my suggestion is and therefore no already have a semantic segmentation model. So I don't know.

D

uh Yeah, okay, uh thank you for the advice and yeah like well. That was one that was my next step like to look see if, if I get any better results or if I can like change the pipeline that which they have given to some extent, so that uh I can make it better and some sort of way like okay, uh like I, saw that code also, and even they have used a kind of a gaussian filter only to remove the noise and everything uh so I'll look at more into it.

D

Also, uh for instance, segmentation. One of the things which was uh like recommended to use was mask or CNN like a a master CNN model. So that is the thing that is the thing I was going to look at because, like, as you said, the conventional models which devoland has uh they. They have a deep learning like imagenet model uh for semantic segmentation, but, for instance, segmentation.

D

uh There is no model with this uh semeda pipeline, which was already given, so that is one of the also uh I I was looking into the segment editing model as well, and I found some like that, and some good resources which all help in inferencing the uh inferencing and uh fine-tuning the model to our data set, so uh I'll share them as well.

D

Thank you for your advice.

C

Because working on the same model would not do your best results if you try to compare with another model with segment anything if we compare both.

C

One segment or anything like last last, two weeks so yeah, that's what my suggestion is. Like you see a other model, my whole project and proposal was completely on segment. Anything only and yeah.

D

I'm looking into Master CNN but I, also uh for my own understanding, looked at segment, editing.

C

What oh, okay, cool! Thank you.

A

That's great Hamachi, thank you for the update.

A

So yeah we want to stop sharing your screen, I guess: okay, So yeah! Thank you for the update. uh Thank you so much for your uh suggestions. um Yeah. We we've been working on uh the Divo, learn, uh upgrading sort of the capabilities of Diva, learn and, and amancio is working on these um topological data analysis, part and uh yeah. This I mean I want to make sure that we have. uh We don't duplicate efforts, so I'm glad that both of you can get together and I would recommend that you know going forward.

A

Is that you and that you know, maybe ask each other or uh see where each other is. You know we'll have these weekly updates, but also you know, um posting things in the uh I guess the Devo learn Divo Diva worm Diva, learn channel in the slack. We can use that to sort of you know kind of make sure that we're not replicating each other's work, because that's if we can use you know, resources that the other person's using or if they have recommendations for things.

A

That's good, because you know it just makes it easier to do things um yeah. So I look forward to next week uh and see what people have uh and so great uh Susan are you uh do you have any updates you'd like to share.

E

Updates um If, someone knows uh how to um get a stress strain curve into the yield portion of the the curve in console. Please let me know otherwise.

E

um Yeah I have uh two models: working three really, but one was made by console and um if I could get my stress strain curve to go past the peak of itself over to the other side of things, then I would have a complete curve that matches the paper that I'm working from so and I have a paper.

E

You know see that oh yeah and you put a force on it and you get data up here and that's all fine. But if you go beyond it, there's two points of course, and the program goes fog, I yeah. This is some sort of unreasonable number that doesn't make any sense. So I don't know what it's doing. Yeah.

A

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My latest okay.

A

Well, yeah, that's that's uh he's a rough spot to be in if you can't figure out from the documentation, that's going on.

E

Because, especially uh unreasonable data.

A

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It's in centimeters and all of a sudden I'm getting meters like 60 meters, oh yeah, I, don't think so.

E

So that's my my issue at the moment.

A

Oh well, yeah we'll see I, don't I, don't know much about console like I said so yeah it's it's.

E

A program that tries to do everything and I think that's what's wrong with it.

A

Right yeah, because I.

E

Keep looking into it and there's all these different things you can do with it and I: don't need it to do that. Yeah, not.

A

That's great well yeah keep us posted on that yeah.

E

Eventually, I'll I've solved a number of problems with it already, so this just seems to be the latest or maybe the final one I'm not sure yeah.

A

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Close I'm getting close to finishing it, but it's just things like that. It's just like yeah.

E

Yeah so okay yeah.

A

A

So yeah, thanks for that, um so today, I'm going to go over a couple things I'm going to share my screen and uh let's see where we are with this. So uh last week we talked about uh like curvatures and cells and and division planes, and things like that. If that does an interesting conversation, uh I might get back to that.

A

I did want to talk about some interesting things: I've found in active matter an artificial life, so a bunch of things I found kind of uh at random this week that people were doing uh so. The first thing is people I've been doing some interesting things with reaction, diffusion, morphogenesis and the things we call Turing patterns and there's this other sort of variation on turning patterns called gray, Scott uh patterns or gray Scott equations, and so this is actually a nice uh PD visualization tool.

A

So basically, uh it's where you have this uh mod, this gray Scott model, which is uh something people have been implementing in web browsers on images, and so this group has been doing this to make visualpde.com, which allows you to explore quite a lot of systems, including Beyond gray, Scott, slash reaction, diffusion models: this is a picture of Turing and he's in a background, and with this application visualpd.com and the simulation you can uh play with the parameters and it you know it'll it sort of modifies the image.

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So the background starts to move and you see things so it basically, you know it can reshape the image or the images.

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The background uh moves around a lot so I don't know if I have a demo of this. If I want to do this in the meeting, but.

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Let me see if I can do this.

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This is a here: okay, visual PD,.

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But sometimes these not work very well in the when you demo them, but.

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Okay, here we go so this is the Turing image, and this is the function here. So it's basically doing these partial differential equations, it's implementing them! Here's the equation! Here you see that it lists the uh equations. You have the definitions, so you can modify the ver uh the parameter values here. The parameters are I. Guess you can look them up here, boundary conditions you can set those so they're right now, they're periodic they can be periodic uh Jewish way, Newman, Robin and combination, so they're different versions of that, both for u and v.

A

So you can see the U parameter here and the V parameter here. It's part of these differential equations and you can set the boundary conditions or both and then the initial condition, which is so for? U and v. You have U it's one and V at zero. That's the default! So you can play with these parameters and you can get um you can make it happen. So, let's see if I can run it from here.

A

Okay, see it's not working! Well, Oh see it's working now, okay, so well you see it come to to the four. It's basically a very light image and it starts to uh gain some form and then some boundary around the edge of the the Buster of the of Turing. And then you have the edges that are kind of drifting outward. The corner is here, so this is morphogenesis of these pixels uh according to this equation.

A

So that's that's kind of a neat thing.

A

So oops wrong one!

A

That's this Tool.

A

So that's the turn. uh The trying reaction diffusion, the gray Scott equations- um actually Carlson did some interesting work on touring patterns.

A

um There's another tool here on carlsims.com, which is the Rd tool and I'm not going to demo that. But this basically shows you some of the things that uh you can do a turing patterns. It's a nice Simulator for this um and basically again you have these reaction, diffusion equations, there's a couple differential equations.

A

um You can use this to understand in this case. It's more straightforward, biological pattern formation. You get these little uh cells that form and these patterns over the spatial array. So you can set the parameters like before it's a little bit different. um It just I think it's basically descriptive parameters in this case and the equation is under the hood, but they have that tool. This is an example of the simulation running, so let me see if I can get it to run yeah there we go.

A

So you can see that it's forming these cells in the middle, the boundaries are growing, so these boundaries are growing a little bit more.

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It's kind of zooming in so okay. What's going on here,.

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So it's doing a lot of interesting pattern formation here in this clip.

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So you have the scale scale, radial skill, random and then the flows parameters here and you can see that it's kind of growing- and you know these shapes- are changing their confi. You know configuration so you can see that it's almost like building like a snowflake here from a initial condition- that's fun stuff.

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um So that's that's great. um This again is the yeah. This is the Turing patterns.

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This one is uh animated reaction, diffusion patterns and flagella. So this is a pre-print uh from the polymaths lab, so reaction plus diffusion equals turning patterns right well, diffusion of Shear, plus reaction of molecular Motors equals animated reaction, diffusion patterns and flagella and cilia.

A

So these single cell organisms- they have these flagella that come out the back, and you know the same thing can be said of cilia in or in cells where they they're these little appendages. That kind of move with where they can move the organism.

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You know they can uh exert forces on the environment or they can be pushed. You know they can be used to modify things if the the cell is moving through a fluid or something. So these flagella kind of move back and forth, there's a molecular motor inside the cell and it's moving the flagella back and forth, and it's propelling the cell with cilia. You often have like this uh layer of the Cilia that can bend with respect to forces.

A

uh If, if a liquid is moving through something or it can be, you know there can be a stiffness in uh instituted by the Cilia or at the base of the Cilia, and you get all these interesting Dynamics. So this is some animated reaction to Fusion patterns. I, don't really have a demo for this, but um there's some really interesting mathematics that come out of this simple uh mechanism. So this flagella is moving back and forth. It's rotating uh and it's generating these waves through the media.

A

But it's also moving forward and you can you can look at all those as pattern: uh pattern formation, so you're, diffusing, Shear, reacting, there's a reaction of molecular Motors, and this gives you these reaction diffusion patterns, so some really interesting stuff there. um This is the paper here, so this is on the bio archive.

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This is the reaction, diffusion basis of animated patterns and eukaryotic flagella, so this is by Cass and Bloomfield gadelia and uh they're from a robotics lab, so they're interested primarily in applying this to robotics, but they're doing this in single cell organisms.

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So this is uh the flagellar beat of the bull spermatozoa and clomido uh clomidomonas rain Hardy, which is a bacteria, can be modeled by minimal geometrically. Non-Linear sliding controlled reaction, diffusion system.

A

So this is uh you know it's one of these systems that generate the patterns we saw in the Turing morphogenesis example, but this is a single cell doing this in a medium model, Solutions or spatially temporarily animated patterns.

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So this is where they're animated in space and time. So, if you have like a little little, you know some some liquid that it's in and it's moving across the liquid. It would produce patterns of the liquid from that movement, uh the describing flagella or bending waves, further connecting beating patterns of psyllium flagella with seemingly unrelated chemical patterns from classical reaction diffusion systems.

A

So there's this basic beading pattern of the Cilia and then there's this chemical pattern from a reaction diffusion system and, if you add those two together, it creates uh some interesting pattern formation instead of chemical species, frequently reacting and diffusing in space.

A

So in the examples we saw of the uh the Turing system, we had chemical species diffusing in space and in you know in Radiance, but this is where you actually have an active force acting against this background of diffusion to provide these patterns, and so our system describes the tug-of-war of reaction kinetics of molecular Motors that are anchored in the flagellar structure, but the shear deformation that they generate can diffuse away.

A

Why a bent the bending elasticity of the flagellum so they're? Actually looking at some of these aspects of share deformation and some of these aspects of reaction kinetics. So there's an interaction there.

A

um Synchronization of the reaction, kinetics and neighboring elements occurs via sliding control mechanism. So this is this mechanism we'll describe in the paper we derived from first principles uh the reaction, diffusion basis of animated patterns and show that this is a direct consequence of the high internal energy dissipation by the flagellum relative to the external dissipation of the fluid environment. So there's this dissipation of flagellum, it's moving against the medium and it's moving the cell and it's producing this, uh these forces into the liquid medium and then there's this.

A

So that's energy, dissipation away from the organism and the and the flagellum. But then you have this external dissipation in the fluid environment, so that energy has to go somewhere um in the fluid environment by fitting uh by fitting, for the first time, non-linear large amplitude Solutions of a specific motor cross, Bridge reaction kinetics.

A

So this is having to do with the motor itself uh in the formation of the motor and the reaction kinetics. That result, we show that reaction diffusion, successfully accounts for beating patterns in both the bull sperm and the climidelmas model. So they have like a regular genetic background for the this uh organism and an mbo2 mutant, which I guess knocks out some aspect of the of the flagellum function.

A

Unifying these distant eukaryotic species under the same minimal model. Our results suggest that the flagellar beat occurs far from equilibrium in the strong linear, strongly non-linear regime and that in contrary to conclusions about small amplitude studies, a unified mechanism may exist for these uh dynain motor molecular motor control. So Dynam is a protein that involves these.

A

That's key in these molecular Motors and you know, provides some of the production of power and motion, so that is regulated by axionemo sliding without requiring curvature, sensing or the fine-tuning of basal compliance and only weakly influenced by hydrodynamic dissipation and the cell body boundary condition.

A

So they talk about they kind of go into some of these things. They talk about reaction, diffusion models and then they talk about the boat of belasov zabatinski reaction or the bz reaction, which is a react, chemical reaction that can form patterns as well.

A

They talk about other non-morphogenetic reaction systems in six and seven, and so there's I, don't know if six will come up I'm interested to know what it is. um Oh, this is actually spatial patterns and ant colonies. This is a group of people. Who've worked on Swarm intelligence and things like that. So that's an interesting paper. They consider that to be non-morphogenetic pattern formation and then seven is dissipation and displacement of hot spots and reaction diffusion models of crime. So this is like human behavior and pattern formation.

A

So they're kind of linking that to some of these other forms of pattern, chemical pattern formation, uh let's see if I can get up to the top here.

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um Let me make a point: your oscillations can persist if a smaller part of the system is isolated without diffusion. So this is where you, if you can isolate a part of the system without diffusion, you can have these oscillations that persist. Coupling the isolated Parts via diffusion can entrain oscillators with non-trivial phase differences. So you you basically around that oscillator you can isolate the system. You can get these oscillations to persist and then, when they get coupled back together, you can get these interesting patterns.

A

This drives, for example, intricate spiraling spiral waving patterns and the bz reactions, and they have a reference for that. However, despite the universality of reaction diffusion systems uh that describe a bewildering array of patterns across science, it is still on clear weather reaction. Diffusion Theory can be expanded to animated non-equilibrium non-equilibrium patterns in nature, such as spatio temporal patterning of self-organized shape-shifting structures, uh the archetype of which is the spontaneous beating of eukaryotic, cilia and flagella. So they kind of get into that's why they picked that model system.

A

This is an image of pattern formation via reaction diffusion. So there's this generic reaction diffusion here, an a which is where you have this, this white and black gradient that come together and, as you know, white is diffusing. Black is diffusing, they're coming from opposite directions and they start to form sort of an interaction.

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So there's like this gray region here at the top and then there's this pattern where they're dots and then there are these kind of uh these sort of nested tracks that you see here uh and then you see dots and then less dense, dots and then finally get to the black. So this whole region of interaction forms different patterns based on the presence of black and white and and what's going on there so and then, of course, you have zebra stripes during development, so those get assembled by a similar process.

A

um This Central striped region here on the top image, is similar to the stripes you see in a zebra, and so that means that there's like this interaction of pigments that goes across the uh skin of the zebra that form these patterns, um and so such animal markings motivated touring when deriving his model system, uh animated, spatio temporal patterns and eukaryotic flagella, is in B, which is here.

A

So this is the uh the cell body, and this is the flagella coming out the back, and you can see that they're kind of animating the movement. So it's moving back and forth and there's some really complex dynamics of this flagellum as it's moving. So it's not just moving back and forth in a deterministic matters.

A

It's actually it's almost like a multi-jointed um oscillator, where you have different uh components of the oscillator moving uh back and forth, and you get a lot of really interesting, Dynamics coming out of that- and this is kind of a model of this where these in these Dynamics here form these striping patterns. So when they talk about the pattern formation of the oscillator, this is what they're referring to these stripes, and these are kind of comparable to what you see here in the reaction diffusion model.

A

uh This is uh see rain Hardy, where you get these two different versions of movement. So um the beading pattern is a human brovine and sea urchin spermatozoa are shown at the top there, along with the breaststroke of two flagella of the green algae.

A

And mcgraction spatial temporal stray patterns. This is what the chymograph is here and then we show can be modeled with reaction, diffusion, Dynamics. So that's where they were going with that they wanted to show the compatibility between those two models.

A

Then you know they have their results. They have this model here, where you have this, uh this is the exonymol projection. So this is where they have this.

A

As soon as this is a cross section of the flagellar axi uh accident, which generates the.

D

A

For this flagellum to move, they have this self-oscillating element, which is where you have a two-dimensional projection of the AXA meme here, where you have the flagella, the flagellum here and the cell body, and it's moving in different directions and it's showing the associated forces with that. And then you have these parts that are connected in parallel down the flagellum and then those articulate with one another.

A

They move so they're, it's like a jointed system, uh so it is like a a complex oscillator with multiple parts and it propagates this wave going outward, but because this thing has a lot of complex dynamics that wave propagation isn't linear, it's non-linear. So you get these non-linear waves that result from swimming forward, just basically swimming forward generating forces using this mechanism.

A

They can generate a lot of non-linear waves, those things interact and they give you the pattern formation that you see in the media. So that's an interesting paper. um So that's that's the part in pattern formation. Then I wanted to talk a little bit about particle Linea, which is a platform that there's a platform called money. uh It's a artificial wave platform.

A

uh People have been using it, it's open source I, believe they've been using it to do uh like the sort of these fluid uh cellular, automata, and so there's some new work uh on particle Linea. It's actually out of Google research and they've been doing things with looking at these uh particle Linea, which are these sort of rounded uh or virtual organisms that move around the space. Like I said it's a like a continuous cellular automata and you can do a lot of things with money. It's a very uh flexible system.

A

I've not worked with it too much, but it's it's really something if you're interested in a lot of things of pattern, formation or other kinds of like Collective behaviors, it might be interesting to play with uh particle Linea is an artificial life form that consists of Point particles that simultaneously generated potential energy field. So the linear organisms are, these are the linear organisms and then particle one is just having these organisms act as particles in a collective system of collective motion and Collective uh pattern formation.

A

So each of these Point particles generate a potential energy field and they try to minimize their own local energy, and so what the point of this is is to show that if you have a lot of these organisms in parallel, you can take a couple of parameters, vary the their value and create a huge variety of different creatures.

A

So you know this is going to have like this each particle that is going to exhibit morphogenesis uh it's going to have an energy field, it's going to interact with its neighbors, and then you can look at some of the diversity of form that results this, as well as the collective behaviors.

A

um This is a Wikipedia stub on lenia, so this is sort of an introduction to lenia it's a family family of cellular or automata, created by Bert Wang Jack Chan is intended to be a continuous generalization of Conway's Game of Life. So if you're familiar with kind Wings game of life, it's the cellular automata, it's this zero player game where you have uh basically uh the soil or automata, that's generating. uh You know different states that move across the board.

A

So people have used this solar automata to generate different types of uh behaviors that they can classify things like gliders and other types of things that emerge from the interactions on the cellular, automata board, and so it's it's basically a continuous version of The Game of Life. So you have the cells which are square and discrete in Conway's Game of Life, now they're fluid in continuous and linear. So these particles are like those squares, and so they can behave collectively they could move, and you can characterize this as sort of life.

A

You know different types of behaviors, different types of morphogenesis and things like that.

A

So as a consequence of its continuous high resolution domain, the complex autonomous patterns or which can be called life forms or spaceships apparently generated in Linea, are described as differing from those appearing in other cellular automata in geometric, metameric, fuzzy, resilient adaptive and real generic I'm, not sure what Med America is exactly, but um you Nick, you wanted to say something.

B

A

Which is okay,.

B

Let's close the cameras, Oh.

A

Okay, okay, yeah, so yeah. They basically just combined in that way and produce complex things um yeah, so they they actually the the gecko conference, which is uh genetic algorithms conference uh lenia won the 2018 virtual creatures contest that that uh conference and received honorable mention for the a life Art Award, a wife 18 in Tokyo, so they've been around the community uh and you know they're kind of well decently, received so uh working with money. uh You know you can probably convince people that what you're uh producing is not. uh You know.

A

People have fewer questions about it than if you Humber something and put it together, um and so they talk about some of the rules of linear. They have these iterative updates, uh which are usually output, States being a pair function of the previous state. Then there are these Global rules representing the application of local rules over every site. So it's it's standard, cellular, automata stuff.

A

You know these State sets that you use, um and then you have neighborhoods as you do in solar automata, so you have the focal cell and then you have the neighboring cells um and so in Lanier's case, the neighborhood is instead of a ball of radius, R centered on a site which may include the original site itself. So this is the ball neighborhood and money, uh as opposed to the more neighborhood in a regular solar automata. So it's just like a Circ.

A

You know a set of circles, so there's a focal Circle and then there's these cells around it or these these circles around it that form a larger Circle. And so um they, you know the neighborhood vectors. Are these set of relative positions with respect to Any Given site? So that's how they Implement that sort of thing, so they can Implement things like this Collective pattern formation in a platform that has rule interaction rules, and then you get these patterns that form.

A

um There are a lot of things: I'm not going to get into uh they're growth mappings. They do link it to the Game of Life um and then there's a lot of related work, which people have noted so other works have noted the strong similarity between cellular or automata update rules and convolutions, and so this is the type of convolution that we're familiar with with convolutional neural networks or cnns, and so these Works have focused on reproducing cellular automata using simplified cnns.

A

There's this aspect of the emergence of self-repairing pattern generation, which can be done with Linea um Gilpin, found that any cellular automata could be represented as a convolutional neural network. So you know we have the cellular automata, they can be represented as a convolutional, neural network and trained neural networks can reproduce existing cellular automata.

A

So we can do everything we do with cellular automata in a convolutional neural network, and then that has implications for say like doing uh machine learning and deep learning, and so these are the wide variety of species you find in Linea. It's very hard to see here, but basically it's these different shapes. You have these.

A

uh You know these Collective structures, they kind of look like microorganisms or small colonies of organisms, even maybe like uh larva or some other or even worms, so they have these shapes that are very lifelike, and you know this relates back to the thing we were talking about before with reaction, diffusion and some of the shapes you or patterns you get from that, and also some of the patterns you get from things like the action of flagella.

A

So uh there's a lot here um and I don't want to oh there's this final paper, one to point out. This is actually uh interactive. Programming, Paradigm for real-time experimentation with remote living matter, and this kind of talks about some of the things uh kind of brings these things together.

A

um We've conceptualized the programming Paradigm that provides stimulus and sensor control, functions, real-time manipulation of physical biological matter, so they're, actually creating a programming system for manipulating physical biological matter. A simulation mode facilitates higher use, throughput program, debugging and biophysical modeling. So they have this JavaScript web toolkit biode that supports real-time interaction with swarms a photo tactic.

A

Euglena cells hosted on a cloud laboratory, so what they're doing is they're playing with these patterns they're playing with these Collective patterns that are formed, they have a programming language that they can manipulate and interact with these swarms, and you know I, don't know how I guess this is just something they're sort of proposing. You know they're, not really they haven't done a lot of cool stuff with it yet, but it looks like they have. It mapped out. So you have you know people using their computer.

A

They have this virtual representation of these cells and the Swarms that they form or the patterns that they form they're able to apply. You know different stimulus, control, functions, biology, sensor, functions, application control, functions, they do image processing, so they need to process the image of the of what the microorganisms are doing and that's that's basically how the program living matter so they're actually programming this using microscopy using a programming language and using different inputs guidelines.

B

Pick your brains or something.

A

B

Adventure under.

A

Three dimensions: right: yeah, swarm simulations are usually two-dimensional, although I think okay.

B

I've come up with a problem which I'd like to call swarms on networks.

A

B

Okay, have you seen anything like that where the swarming behavior is confined to stay on the network rather than to a doc.

A

uh But actually I mean maybe some of the ant colony, optimization work that people have done is kind of like that, so they do like a lot of time like yeah.

B

A

So you have answers the nodes and then the the edges are like pheromone Trails or interactions between them.

B

Oh yeah yeah, in that case the uh what we call them. The uh the active units are creating the network I'm talking about swarm on a fixed, Network.

A

uh I, don't I, don't know, I mean there probably is but I don't I, don't know what the reference.

B

A

B

You see anything like that, I'd be interested, it's actually a computer.

A

Geography problem: oh okay, yeah I'll, take a look. Yeah I, don't know if there's anything.

B

In other words, the the motion of each of the.

B

What do you call them the active units or uh is confined to stay on the network.

A

B

Okay, the the end problem is not the same, because they're they're creating Network.

B

A

Yeah yeah I'll take a look and see what there is out there.

B

Okay, I appreciate that yeah.

A

Yeah, a lot of these simulations are inherently in 2D, but I mean like the lenia and then, of course, the reaction thinking of sworn Behavior birds and fish and stuff like.

B

B

Everything is fixed, then you can well your units along okay, okay,.

A

Yeah I'm not sure how, like in Millennia case, it's a continuous cellular automata. So we usually think of that as a Contin or a discrete system where you have cells that just kind of interact and the interaction determines the state, the subsequent state of its neighbors. So it's like if something propagates. It's usually like this so interacted with this cell and influenced it, and that on and on with.

A

B

Okay, that's what's different: we can still interact across edges of the network, protect uh they can't jump from one to the other. They have to stay on there on the network.

A

A

Yeah exist, the existing Network yeah.

B

A

That's an interesting idea: I'll have to look.

B

A

B

Networks of Christmas tree light bulbs: oh.

A

Yeah I remember that problem yeah yeah.

B

In that case, you can enjoyed.

A

Okay, yeah yeah; okay, when we get to move move along the wires.

B

This is a big problem right, more serious work, yeah.

A

Yeah some himanshu had a comment here um yeah, so the problem formation of swarm on network seems interesting. Since the interaction leads to step to the step, then there can be a Markov assumption that the current state only depends on the previous state. Yes, there's generally in cellular or automata, it's like a Markov process.

A

There isn't usually a memory, um it's just kind of like that's. Why you have these patterns that kind of diffuse and they're sort of fleeting in Conway's Game of Life. You have to have things like gliders that move across the screen and then they disappear, and so you get like this, you know you have to like be care. You know you have to watch the thing, find a pattern and then classify it, they're very um itinerant in that way. So, but you could like Implement a memory on that.

A

um It's just that the I think the kind of the premise of cellular automata, though, is that there isn't a memory, because if you have a fixed memory, you end up. You know basically crowding yourself out. So if you uh I know, hamanchi has worked with agent-based models.

A

um If you have an agent-based model, where you have a bunch of agents and they're interacting and they kind of form clusters or something in space uh and if they're not like you know, they kind of, can the algorithm converges so they kind of stick there and then, like you, can't move it anymore like there can't be any more pattern formation, because the patterns are already kind of fixed.

A

They just don't have any room to move the same thing with like chemical diffusion, where there are chemicals that diffuse and then over time they run out of energy and the patterns kind of either stay.

A

You know kind of State static or they just kind of dissolve, and so at some point you run out of that capability, and sometimes you know having more energy or not having a memory of what came before actually helps you create new patterns so that that's an interesting point and I don't know like what the answer is there I don't know if anyone's worked on like uh memory filled or memory capable uh cellular automata, but I know that by default, they're memoryless, so they're Markov.

B

A

B

Okay and there's another peculiar one.

B

Of the processes where the memories of the previous state- and so you don't interact with the current state of other things, you have you interact with the previous data.

A

And this can drive the system into weird kinds of oscillations.

A

Okay, yeah, okay,.

B

I think it was studied in the 60s and differential equations with time delay between the uh differentiating pardon and what happened previously.

B

You know versus the state the current state, the change in the cards that God depends on the current state is.

A

Spending done previously yeah. Thank you.

A

Yeah, it's an interesting thing and we were looking at that example from the flagella. You know you have all these non-linear dynamics that are coming out of the flagella's motion. uh I mean there's a memory there, but there are interactions from previous States like.

B

A

Something moves around you get these waves, that kind of Collide, I, guess um yeah.

B

Yeah I guess you wouldn't have memories, because the momentum is not important right.

A

So finishing up on uh amanci's comment, uh this seems like a good problem for an earl-based approach. Yeah. It would be interesting to put Implement an RL like some sort of RL, Solo or automata combination. Where you know uh the cells are picking the best policy and you know, then they share that information with their neighbors or something I'm, not really sure what that would look like, but um it would be some sort of policy learning and then the policy would the selection might be like my neighbor selected.

A

This and I'll select this as well, and then you know you see what happens set of rules, because the cas usually have these rules that they follow, but they're very simple interaction rules. So it's like if your neighbor does, if your neighbor shuts off you shut off uh or if you shot if they shut off under a certain set of conditions, you shut off as well.

A

It's not really that deep in terms of uh like a uh you know, function it's just basically a simple thing that it's just following copying: Behavior, it's not really like in depth, um but yeah I mean that would be interesting to have that reinforcement, learning aspect to it as well. So you'd have this. uh You know. You'd have probably have to have some memory as well for it, but um yeah I, don't know.

B

um Bradley, let me have one other point. A lot of these things are very neighbor depend right. Dependency depends on the size of the uh something like pixels or voxels.

B

Okay, I came up with the method many years ago, uh which is sort of independent of the local scale uh and uh I called it. Adaptive neighborhoods.

A

Yeah: okay on adaptive, neighborhood.

B

It was used for image processing and we're basically calculating the contrast around the pixel versus the scale of the of the region around it uh to give it make That explicit. Supposedly, you know ordinary deal with a three by three neighborhood, a round pixel. Okay, what we've made it is three n by three half.

A

B

And then what you do is you calculate the contrast between the pixel and that surround versus the size of the surround and if you calculate that, to get a function which goes to a maximum and then sort of goes all over the place.

B

So what you do is you pick the first Maximum and we call that the Adaptive neighborhood for that pick and then you could operate on that by changing the contrast, through whatever you always pixel, okay. So let's get into a skill and it's sort of I think it's sort of a scale Independence, uh probably the size of the smallest pixel that you're using for your array: yeah: okay, because it uh uh the it's picking what what scale is best for that for the local region of that of that pixel.

B

Okay, yeah so, and it led to interesting image. We were using it for uh increasing the contrast in images. There was an old technique in mammography called zero mammography, which was basically a xerox machine that that works on mammograms, and that's that's where the idea came from that the uh the zero bandogram actually works with the physics of the electrons of the the plate that formed the image yeah.

B

B

If It produced sharper images with the sharpness was related to.

A

The local scale, okay, yeah.

B

Okay, now I die, I, don't know you know, for agent systems, I'll be curious to see if this had an effect right. The words of an agent depended not on just labor but depending on its adaptive neighborhood rather than three by three. They break.

A

A

Yeah it'd be interesting to see it's kind of cumbersome, but it's uh you. You know you went to a three by three neighborhood and then Mine.

B

By 27, by 27 or whatever, okay yeah.

A

B

You plot this contrast versus the size of the neighborhood. When you picked the first Peak.

A

B

So it's this conceptually, it's not too complicated. It's.

A

Actually, but it's a lot of computing right, yeah.

A

um Yeah I know we did things with um I, don't know if this is no. uh The morphozoic stuff that Tom was working at has been working on.

B

A

It doesn't use adapting neighborhoods, but it uses like a different definition in neighborhoods than you typically see in a discrete cellular, optometrist yeah. It's not really adaptive, it's kind of like nested I guess so you have these smaller neighborhoods in these larger neighborhoods.

B

Which, of course, could change with time.

A

All right: well, that's good.

B

I might be curious.

A

Yeah all right.

B

A

Go ahead yeah, maybe you can reformulate.

B

Some of these aging problems in terms of death, Amigos.

A

Yeah yeah. That would be interesting.

B

See how they behave, yeah.

A

So now I'd like to talk about a few other papers, um but first I'd like to do a couple of the demos that I didn't do when we were in the meeting, because it tends to lag so um the first one is this reaction diffusion tool. This is the Carl Sims website carlsims.com.

A

As you can see, we have this pattern. That's forming I showed the movie where you start you can regrow, so it grows from a circle and then screwing these uh fractal patterns throughout the space here and then those the insides of those fractal patterns are changing their shape and you can see that, like some of these interior cells, you know things are being defined sort of in different ways.

A

So there's definition of almost looks like a maze, is forming a lot of those undulations that were originally that resulted from the circles. You see this sort of snowflake pattern, that's forming, and then you see these deepening furrows that look almost like a maze is forming here from the central point. So this is this is how this sort of reaction Fusion happens. You can vary the pattern in the simulation, so I can regrow it according to like the stripe pattern.

A

So this is where you start with a single point and then it diffuses across the space and again you have these uh these long boundaries on either side, but in the middle you have these dots or these uh sort of uh lumps of whatever this is, and it looks like they're dividing and there's this pulsing in the middle, that's sort of where it's just kind of like there's. A lot of I think there's tension on the surface, so um dick mentioned that you know, there's a difference between two dimensions in three dimensions.

A

So we see here is the two-dimensional case where we have up and down and left and right, so it can diffuse across this two-dimensional space. The forces can act along this two-dimensional space. So you have this two-dimensional gradient. Basically, you have things happening in the middle. You have things happening on the edge, the other things happening on one side versus another, but it's always a two-dimensional aspect and of course, as we know, uh biology and tissues in particular exist in three dimensions.

A

So this is not three dimensions. This is two Dimensions, so the question is: what is a three-dimensional system like this look like, and the answer is, is that it may be that it's just kind of a spherical version of this or it could be very different uh depending on how far you are in terms of the layering from top to bottom.

A

um So you know this is this is how you get pattern formation say in embryos. You have this local pattern formation that leads to Global. um You know heterogeneity, and then you get those systems integrated over time, so yeah. This is a nice simulation from Carl Sims.

A

This is an example of the gray sky uh reaction, effusion system, so the gray Scott system is a little bit different from the Turing system, um so the gray Scott system is a reaction diffusion system. This means that it models a process that consists of a reaction and a diffusion. So the reaction is some chemical reaction that transforms something. So it's usually some sort of reaction that takes in energy. It produces an output, and so you can see with the expansion of some of these objects.

A

In the in in the Carl Sims simulation, where you have this growth, that's going to be a reaction. Your diffusion, on the other hand, is how these things spread across space over time. So it may be chemicals that spread across space over time or it could be particles that spread across space over time or it could be a cell that expands and then divides a number of things that are involved in diffusion.

A

So diffusion doesn't necessarily involve energy, although it could, but in general, if you're diffusing, your your energy function, usually minimizes from the with respect to the distance from the source of that diffuse process. So you might have a chemical Source like a cell and then you, as you, move further away from that cell. The amount of chemical diffuses until you go to a point where it's almost nothing and so I can draw this out.

A

A

So if I draw this out, I have a source.

A

Which is a cell and I have a two-dimensional space where things are diffusing and that diffusion function usually is maximal at the source of the cell. It minimizes as it moves away from the cell.

A

So we're considering this diffusion along from left to right here, and so this this, whatever factor is being generated by the cell. It that's an output, and the input, of course, is energy.

A

So there's some reaction in the cell and then there's diffusion going outward, and you can couple these. uh You know through the consumption of energy, the production of some reaction in the cell and then the fusion of the products of that reaction moving out finally getting out to an edge where it's almost non-existent.

A

If I looked at a system of two cells, you can see where we get these gradients. So if we sell the cell on the left and the cell on the right, they have their own reactions. Maybe it's the same reaction.

A

There's diffusion outward, and this is again linear, diffusion and uniform, mostly so there's a set of concentric circles.

A

That sort of you know at each circle there's some decay of that product and the environment and then eventually become. You know this decreases almost to nothing, but the important thing here too, is that, as it decreases to nothing if they're close enough, there's this region of sort of interaction for overlap between the two products being produced and so that region of overlap is usually the sort of the edge of these uh radians. So in uh current reaction diffusion, we often speak in this language.

A

A pattern formation and the patterns are usually stripes, so it can look like this. Maybe we have stripes and the stripes really result from the edges of these diffusion, cones or whatever you want to call them, basically, as those overlap, those those boundaries sharpen and they produce some sort of striping pattern, so you might have Source cells in middle of each of these layers, like we saw with the example of the black cell and the white cell and their interaction, there's diffusion in from coming from both directions towards this boundary.

A

This boundary represents the intersection of these two uh diffusion columns and then that sharpens the boundary between them because they interact, whereas they don't interact. If you're, you know, if they diffuse say up versus down, they won't necessarily diffuse. When you have something like that, because they're not coming into contact, those products are coming into contact at the boundary and then that's when you get a sharpened boundary, which is usually maybe a change in pigment or like a combination of two chemicals, uh and you can usually see it as a pattern.

A

So that implies that this process happens in parallel from you know, left to right or right to left. But this is all two-dimensional and so I think that's an important thing to remember um now. Grace God, of course, is uh a model that where reaction is a chemical reaction between two substance c1v, so those substances in this case will diffuse over time during the reaction U gets used up while V is produced. So this is interesting that you have?

A

U and v U is transforming and maybe into V uh U gets used up, so there's a pile, a stockpile of U and that gets used up in producing V and V might be produced, maybe semi-independently view. But you get this. Basically, these two storehouses a view and v? U.

D

A

Used up, V is produced and they both uh diffuse across this two-dimensional system. The densities of the substrate? U and v, which are now small, U and small V- are represented in the simulation which is down here.

A

um So the gray Scott model models, the chemical reaction, U plus 2v to 3v. So basically U is added a 2v and it produces an extra V. The reaction consumes you and produces V. So you have this. You have U. It gets added to a feed rate which isn't shown in this equation, but the feed rate is basically how much you do. You need to produce a multiple of v, and so that's what this is. uh So this is done by adding you at the feed rate, F and you're moving V at the rate K.

A

So you can also remove V from this through the.

D

You have to kill.

A

V or you have to it, becomes a sink. It basically gets used up, so both of these can be added and used in different ways, and so basically it's where you have these stockpiles where you get production that produces this thing, you get a kill rate that reduces this thing, and then you of course, it's transformed to V. You gets used up in the surface of v.

A

um This feather chemical reaction, V transformed to P, is where V gets turned into a product p, and so p is an inert product which can be. You know, basically something akin to thermodynamic entropy, where it gets basically locked up like on energy that can't be used. It does represent work of V, so that's, but the important thing to remember is V is not available to diffuse.

A

In this case the parameter. K controls the rate of the second reaction.

A

um Both substance is diffuse over time at the diffusion rates, d, sub U and d sub V, and the simulation down below here d, sub U is double d. Sub e. This ensures that patterns can actually form, and then you can control the feed rate and the kill rate in the simulation. So this is a simulation.

A

uh This is the color here. uh The feed rate is here, you can modify it. The kill rate is here so basically, if I have a high feeder and a low kill rate and then I get this, you know speeded up like 3x, so I can get this moving, um and then we start the simulation and I. Don't think anything's happening it's like what do we do decrease the feed rate increase the kill rate a bit and speed it up a bit?

A

Okay, we overshot. Again, uh let's see, let's go down to the kill rate of about 0.01. Sometimes these parameters have to be pretty small. Get these things to work.

A

B

Right there we go, it does.

A

Converge pretty quickly, so uh let's try this okay. So that's it's just the circle, that's expanding!

A

So let's, let's do this! Let's increase the feed rate.

A

To about that, okay, now we're starting to get some internal structure. The feed rate is about 0.126, the kill rate is 0.01, and actually now you get a stable pattern that emerges so you get a feed rate. That's maybe in maybe an order of magnitude higher than the kill rate. I. Guess that's what it would be and then that's what you get you get the stable pattern, that's fluctuating if I increase the kill rate more that that pattern starts to change yeah.

A

So if I increase the kill right over like 0.04, it basically kills my pattern altogether. So this is the feed rate higher in the kill rate, but still you get these patterns and if I increase the feed rate even more and I start. This pattern really starts to like you can get the entire black area to segregate out of them. Well, it doesn't really stay that way. Okay, it's something like this! So This! Actually, okay, now it's stable.

A

So this actually looks like um something you might see in the belt uh Alice Savage reaction or the bz reaction. We talked about in the meeting in the main meeting that you get this these sort of patterns. Now it's stable, you get this.

A

These uh I don't know what you'd call them these little segments in in the soup, and so this is stable, a feed rate of 0.187 and a kill rate of 0.023.

A

So it's interesting to play with these parameters and see what differences you get. One of the the takeaways from this is that, depending on the kill rate and the feed rate and the combination of the two you know when you're running through the equations of this model, you can see that there's a larger amount of variation in the output. On the other hand, you can blow it out pretty easily you can get if you increase the feed rate over probably over 0.2 and the kill rate over 0.04 yeah. You know ceases to really do anything.

A

So it's really interesting how these parameters get tuned. They have to be pretty low generally, but the feed rate has to be higher than the kill rate. That makes sense, because if your kill rate is just like your entropy, so it needs to be a background number with respect to the feed rate. Feed rate needs to be high to keep the system supplied with energy, so this is a nice little. uh This is the theory here below. So this is the differential equation, uh a couple differential equations, so you have.

A

This is basically a I think it's a partial differential equation, as you see with uh the term morphogenesis, um and this is the setup for it. So you have the feed rate here. You have the kill rate, which is here so this one is death. This one is birth and this has a lot to do with and I think in particle one year. uh They brought up the idea of um Predator prey equations or it could have been one of the other papers where they took out predator pre-dynamics and.

D

A

Essentially, that Predator prey Dynamics, you get the burst of the different two different species: they have a birth rate and a death rate, and so you have to when you play around with the birth rate and death rate, you get a pattern of uh Predator prey co-evolution, where, if you increase the amount of Predator, you decrease the amount of prey, but then, as the number of prey decreases, the number of predators and that cycle can can continue at infinitum if they're at equilibrium and the trick is finding the equilibrium.

B

Values and that's kind of what I.

A

Was doing here with the feeder and the kill rate I was trying to find the equilibrium point, the feed rate being analogous to reproduction, the kill rate being analogous to death in the Predator prey model.

A

So that's a little bit about the gray scout model. um Then we can talk about particle linear. So this is the Google research paper for particle Linea. uh This has a video associated with it, so it kind of shows the you know how this works, so I can just mute it. This kind of goes over particle, linear and the different patterns.

A

So this is these: are the little uh cells Simple Rules, so they can divide, combine or actually I, think they're, just dividing in this case, and you can see that they observe these Simple Rules, so they divide, they form these morphologies. These clusters, they're coming from the edge I. Think- and you know it looks almost like an amoeba or something like that- maybe like a volvox moving around these are just these aren't real species they're just creatures that they're creating they can create other things like oscillators, where there's an interior part of.

D

A

Cell there's an edge there's, a potential energy field that you see, and these are just like based on the rules, so the rules are creating these fa energies or these fa forces, and it's it's producing things that are lifelike, it's producing things that are like how forces act upon the cell. Now these are gliders, and these are the things you find in The, Game of Life in particle Linea, there's a version of liguire that you can identify, and so these things are actually pretty itinerant. They're.

A

Not they don't stick around that long, but you can observe them in the system. So now this is a steerable glider, where it's bouncing off the walls. It's very interesting stuff! um There's a demo here that you can download. That shows you these.

A

Yeah so I think that's a good example of kind of the things that we have here. These are mathematical waveforms.

A

um So, let's consider a simple idea matter consists of tiny, constantly moving particles which attract each other close distances but repel when they're too close, we can use Leonard Jones potentials as one possible mathematical formalization of this, in spite of the apparent Simplicity of microscopic Dynamics at large scales. These rules give rise to a plethora of complex phenomena such as aggregate states and matter thermodynamics, Acoustics, hydrodynamics and turbulence in scientific and Engineering practice.

A

We can often abstract microscopic details behind macroscopic models, so we can use things like diffusion or the navier Stokes equations that operate at the scale of Interest. So we could use these types of things to sort of get at you know if something is operating at the Single Cell level or the level of the external environment or the level of this little Colony. We can use different models to model these these phenomena, so we talked about uh multi-scale modeling in past meetings, and this is kind of where that fits in.

A

So this is this is smooth life. This is a continuous cellular automata. We just do some really interesting things with this. There's linear and then there's full linear, so flow Linea actually tries to work around the issues that Linea has with conservation laws. So money often has observed explosive growth or Extinction behaviors. We talked about explosive growth being a consequence of runaway positive feedback, and so we want to try to regulate some of these systems a little bit better.

A

Sometimes that's that's partially because they're, you know, the laws of physics aren't fully modeled in these systems, but we actually do use uh partial differential equations here, as we do with some of the reaction diffusion models, but you still, you know you have problems with like the conservation of energy and being totally consistent with that. So flow lineage tries to work around this by formulating the partial differential equation system around a flow field that moves the distribution of matter in space without creating new Mass.

A

So it basically is trying to. uh You know, specify these conservation laws a little bit more um then, in this paper they also propose a method of combining multiple update rules in the same space. Particle Linea can be seen as an as another perspective on the flow linear model. We represent moving matter as a population of particles rather than as a scalar field. So that's interesting. You can actually implement this as a field, wide phenomena and a lot of simulations. We do that, but that ends up allowing you to treat it as a uniform Force.

A

So you can have a uniform set of forces across your simulation. In this case. It's it's. uh You know a property of the particles or a property of a population of particles. So you don't necessarily have this aspect of the uniformity. It can be more heterogeneous, so they have this stub lagrangian Flow versus eulerian.

A

So this is uh lagrangian versus eulerian specification of the flow field in classical field theories. We use a lagrangian specification, so we look at fluid motion where the Observer follows an individual fluid parcel as it moves through space and time plotting. The position of an individual parcel. Through Time gives us a path of the parcel. So this is like you know if you've ever seen: um lagrangian, coherent structures and some of the analyzes that come out of that.

A

It's where you have an initial particle with an initial state and then you track that particle across its Evolution and sometimes you're tracking the two particles as they diverge. So you know there's a whole set of equations here. But to make this simple, you have an initial condition, which is a particle and you're, basically tracking its position through time, and so this is the time evolution of this particle um I'm on five. Actually, okay.

A

So this is the you know to make things simple. You have this initial condition this particle here you have the time Evolution. The particle ends up here over this time, so their physical forces acting upon it but oftentimes in the lagrangian formulation, you're just interested in a uniform uh set of physics and you're just interested in this trajectory.

A

You might have another trajectory here in uh in LaGrange income here at structures, you're interested in some of these divergences between the particles over time.

A

So there are ways that you can calculate that and then, if they end up in like a ridge or some other cluster, that means that they've all evolved sort of along the same set of trajectories. And so then you can make that calculation and explain that there's been this diffusion of particles over a certain amount of time in a certain direction.

A

Now you could actually use if uh another method, which is to look at the evolution of these particles, is a property of the forces and things like that, and that is more a lot around this hilarian uh specification of the flow field.

A

So the eulerian specification is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the river pass, a fixed location.

A

So, in this case, on on in our space, these arrows represent these fixed locations and you just record the what what's going on at those points and so you're not calculating the trajectory from t 0 to TN you're, calculating them at different points, and that you know that gives you this sort of heterogeneous view of things um and then so. The lagranging name you learn. Specifications to the flow field are sometimes Loosely denoted is a lagrangian and eulerian frame of reference, so they're different frames of reference for this.

A

uh However, in both the general General, both the lagrangian and eulerian specification of the flow field can be applied in any Observer. Certain reference in any coordinate system within the chosen frame of reference, so they're different frames of reference, one is sort of at the end of the process.

A

The other is during the process and those are different points of view. Sort of you know how you choose to look at the problem. uh However, you can use a common set of coordinates average either you know set of conditions or either you know set of points of view, and it doesn't matter it's it's invariant to that. But we do have this so we're using this eulerian specification as opposed to the full gradient specification.

A

So that's a uh I guess a summary of some of this stuff they're doing at flow linear and particle Linea is.

C

A

Really interesting approach: um there are quite a few well-known particle-based, artificial life simulations, including classic Boyds, primordial protocol systems and many others. So uh this one primordial particle systems comes from this paper in 2016. How will lifelike system emerges from a simplistic particle motion law, so this is kind of going through some of these individual things that you know this sort of model so voids is as a model of collective flocking. Amongst these virtual words, they call voids.

A

uh This is uh a basically simplistic particle motion law, so it's very similar to that, but it gives you these lifelike uh forms. So self-structuring patterns can be observed all over the universe, from galaxies to molecules the living matter. If their emergence is waiting for full understanding, we discovered a simple motion law for moving and interacting self-propelled particles leading to a self-structuring, self-re-producing and self-sustaining lifelike system.

A

So these patterns emerge they resemble living organisms, it's always about resemblance. You know we can't necessarily verify whether these things actually have anything beneath and in fact that's the idea it doesn't have to have like internal mechanisms. It doesn't have to have Consciousness or sentience, or any of that it just needs to look like a lifelike system, and so in that sense we can use basic physics to do this, um but this is you know this is again just describing these rules of interaction.

A

um The general generality and simplicity of the motion law provokes the thought that one fundamental rule described by one simple equation, yields various structures in nature. It may work on different time and size scales, ranging from the self-structuring universe to the emergence of living beings down to the emergence of atomic formation of matter. So it's also important to have the sort of universality aspect to it, and so they provide pseudo code, but they show there's Collective behaviors for these particles and densities.

A

You can see that they're, these different patterns that we've reproduced uh in the gray Scott model. There are different types of pattern: formation that occur.

B

A

Out of these uh particles and physical forces acting on them, uh there's no magic, it's just the interaction of forces, um and so this is, let's give some examples. These are some more examples here of spontaneous emergent and expansion of lifelike structures into a density, regulated ecosystem. This is where you have this.

A

uh These different biological rules, such as division, birth of the population, expansion and sort of how the whole habitat is covered by these particles.

A

um So it's you know it's kind of reached its limits of expansion, um so we can do all these sorts of things that are kind of lifelike in in their sort of Nature and we can actually produce life-like, behaviors um and so there's a lot of uh a lot of mathematical modeling in here for like density, dependent growth and things like that. This is still in a two-dimensional space, but at least now we have these different conditions that are kind of like what life experiences and we can actually reproduce these behaviors.

A

um So there's a lot of you know: there's a lot of sort of State dependence, so oftentimes you're, starting from an initial condition and you're moving towards uh some sort of self-organization, but it's always dependent on the initial condition, as we saw in like Ray Scott simulations that it's hard to sort of get the initial conditions right. But then, when you do, you can often find equilibrium where things persist for long periods of time.

A

And so uh you know, this paper is I'll post these papers in the slack, and uh we can talk about them more and hopefully this inspires people. Maybe to do some really interesting work.

A

So thank you for paying attention and I hope. You learned something okay! Well, if there are no other comments, then uh thanks for attending and uh good luck with uh your weekly uh gsoc activities and talk to you next week.