Cellular Automata

Considering all the weird problems in mathematics, and all the weird behaviors in CA, it's hard to not think that there might be some rule in some CA that connects a problem with its solution.

Like imagine if numbers could be converted into cell patterns in such a way that a certain rule will cause that pattern to evolve into its corresponding prime number.

Cellular automata can be used to generate pseudo-random numbers, and it is also useful as a teaching tool for logic because it gives a visual interpretation of logic which is usually taught strictly as relations between symbols. In a way, cellular automata is to logic as geometry is to algebra.

Also worth mentioning, while cellular automata themselves may not have any direct applications besides generating pseudo-random numbers, techniques developed to analyze and classify cellular automata likely will ultimately have direct applications outside of analyzing and classifying cellular automata. Tools made to study one thing end up being useful for something else even if the first thing being studied is useless. I don't know how often that is true, but it is probably true enough of the time to not altogether stop studying useless things.

tcm.phy.cam.ac.uk/~tmf20/PUBLICATIONS/epl_08b.pdf

>When are cellular automata random?

>A random cellular automaton is one in which a cell’s behaviour is independent of its previous
states. Analytical conditions for the existence of random cellular automata are derived and we
find that a multitude of non-trivial random cellular automata exist. We develop an indicator variable
formalism to further investigate these random automata and confirm analytical results with
simulation.

life really isn't that interesting

there are some cellular automatas (many, actually) that just blow up to arbitrary size with amazing complexity after you give them around 8 bits of data

Life is interesting because it is Turing complete system, but I agree there are many different CA's which deserve just as much attention

Many of the ones that blow up are turing complete too

There is this one based on Sierpinski triangles that form when you put down one square that is turing complete as well

How about sandpiles?

youtube.com/watch?v=1MtEUErz7Gg

The weird "zeroes" of sandpile sets are pretty cool.

I myself don't know of many applications for older CA like Life, but I do know that it directly resulted in the development of agent based modeling programs. There are whole coding languages out there written for the purpose of modeling complex adaptive systems using principle similar to those you'd find in CA. Some of them have even been found to have predictive power( mostly in ecology).

man, I got excited when I first saw that book, then I realized it's like 1000 pages of himself auto-fellating

Which one? I wasn't aware of this possibility...

Fool, the ultimate CA is in imaginary dimensions.

I wonder about CA being used as a hashing algorithm.

Encode input data as initial generation. Perform N steps of cellular autiomaton. Pick out a non-trivial segment of the result, save as hash.

>Encode input data as initial generation
>Perform N steps of cellular autiomaton
>Pick out a non-trivial segment of the result
>Use result for new input data as initial generation
>Perform N repetitions
>Save non-trivial segment of the result as hash
ftfy

Can someone explain to me exactly how the Wolfram language and Mathematica uses CA?

Mathematica doesn't use Cellular automata directly. I think it uses it for a random number generator though.

>Can someone explain to me exactly how the Wolfram language and Mathematica uses CA?
To make cool images.

People kept telling me that it was somehow using CA as some core part of the language.

We haven't even figured out how to define negative dimensions yet though.

Wolfram wrote a book saying that any system in the universe could be simulated with CA.

Look up A New Kind of Science

Meant for

>People kept telling me that it was somehow using CA as some core part of the language.
I'm shitposting.
The point is, Stephen Wolfram is not humble in presenting his language and CAs.
Yet I've not heard of any groundbreaking discovery in physics involving CAs.
Let alone CAs being a new science.

youtube.com/watch?v=sHu2RQLQba8

Saw this 8 years ago, asked in the comment what rules he used, never got an answer for years, eventually forgot about it.
Found it by chance recently, my comment is not there anymore (probably cause you didnt need google account back then, and they probably deleted the unregistred comments), the uploader answered some question 4 years ago, if my comment was still there he may have answered.

mfw.

The sierpinski triangle ones come from Wolfram himself. he has this one paper about doing cryptography with them

The others are just ones that I have found when playing with CA rules

>Yet I've not heard of any groundbreaking discovery in physics involving CAs.
the first successful attempts to simulate fluid/group dynamics on computers have almost exclusively been CAs

>Let alone CAs being a new science.
Noone has stated that. But with WolframAlpha, Stephen Wolfram tried to treat CAs as a holistic system rather than a niche application. His Language System can do very complex computation with precise results not losing accuracy when getting converted into different types of data.

>Noone has stated that.
So you're that Wolfram shill.

I always saw CA as an oversimplification of the real world. Sure, urban sprawl, bacteria, or anything observable across related dimensions behave like CA, but not "our" CA.

I wrote two CA apps. One with non-square grid and one in assembly. It's fun, and experiments can yield cool phenomenons, but it is not real.

>apps
fuck off with your apple zombie buzzwords

it's a program, not an app

>Wolfram
>mfw a priori art isn't a thing anymore

It's meh to shit. Big problem is the grid. Physical discrete systems don't live on a grid (even crystals have defects), and it's grid dependence makes it a poor substitute for continuum methods at higher length scales.

It's fast though.

Yeah, the "muh grid" problem is a kind of depressing limit.

Hey, I'm the creator of this game. Thank you for mentioning it.

There are "continuous" analogues of cellular automata:

en.wikipedia.org/wiki/Continuous_spatial_automaton

I think I saw it here originally, I've spent a surprising amount of hours on it since then, kudos for a great game (soundtrack is also fantastic by the way)

Cellular automata can be very useful in materials science, especially in combination with finite elements method to model solidification, spinodal decomposition or fracture behavior.
Pic related.

>His Language System can do very complex computation with precise results not losing accuracy when getting converted into different types of data.
But it doesn't actually use cellular automata to do these computations right?

If we do live in a simulation, it is probably running on a C.A.

I did post it on this board awhile ago, you probably saw it then. I'm glad you like it - thanks. I put a lot of thought into the soundtrack, so I appreciate that as well.

>CAs that don't follow the exact same rules as other CAs don't behave exactly the same
Perhaps this is not too surprising?

I don't get the hate for Stephen Wolfram. It seems very academic and petty.

sounds like that's not really cellular automata

an attempt to simulate an apple by writing a program to simulate an atom and then running it 2 billion times != cellular automata.

not a bad book

I think I like Wireworld better than Game of Life.

Despite having more than two states, Wireworld somehow feels more elegant (as there are fewer rules). You don't get as much "chaotic" behavior as one might get in Life, but honestly, that stuff gets kind of old, and sometimes you just want to move past that stuff and get your hands dirty with logic constructions (which is easier in Wireworld).

There is another very interesting application I'd like you to see:

tones.wolfram.com

Music Theory was a untouched field for CA application before Wolfram and shows once again that a universal computation can be possible.

a universal computation language*
*fixed

Very cool

Will look into it, you got a link to the PDF maybe?

you can build a computer that is completly reversible using cellular automata and the billiard ball model from tofolli

With this thing you have a machine where you can go back in fucking time

If only there was some rule that allowed you to tell, whether an arbitrary computation can be realised within a system, maybe some way to reduce the system you are considering to one that you already know is capable of such a general behaviour? Someone should investigate that.

Is studying cellular automata the final frontier of autism?

No it doesn't, but OP will ignore this and keep spreading his nonsense.

WHAT IF

Cellular automata

On a hyperbolic grid.

ofc the core code (memory management, CPU Usage etc.) is written in a common programming language but all higher level functions are handled by built in rule based programs which work with abstract expressions, which is nothing less than non-visual CA. It's not magic and has been done before, one just doesn't see fancy gliders or fractals.

>A foundational idea in the Wolfram Language is that all expressions—whatever they may represent—ultimately have a uniform tree-like structure.

If you still think I'm wrong enlighten me please.

Jesus that sounds awful

CA Model for measuring oil percolation as a function of soil porousness

That sounds like it still needs a LOT of work.

do you have a source on that?

They definitely have been studied:

sciencedirect.com/science/article/pii/S0304397502006606

Its a screenshot I took from the program it runs from

ccl.northwestern.edu/netlogo/models/Percolation

The Schelling model is one of the most famous CA models.Schelling developed it during the 1970's as a way to model racial segregation in the US.

Each cell is set to want to live around a certain percentage of cells with the same color as its own. If there are too many of the other kind of cell around, they move somewhere else, affecting the proportion of the neighborhood it just left as well as the one it moves to.

The emergent property of the model is that the total level of segregation is much higher than the preferences of the cells would denote : for example, in most simulations, if each cell prefers that at least 30% of its neighbors are the same color, the average cell actually ends up having 75% of its neighbors of the same color.