Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [cellular-automata]

Questions on the usage of CellularAutomaton and on custom implementations of cellular automata.

0
votes
1answer
77 views

map cellular automaton to planar surface

Im exploring possibility to apply a CA to a portion of a region in an image. Think that I can process an image to identify a region, as an example, a green area. I would like to confine that area, ...
10
votes
1answer
129 views

How to solve (O/P)DE via cellular automaton?

I heard that one can solve differential equations by a cellular automaton. Even though I have searched some papers, which seem too formal to me, I do not get the hang of it. Anyone knows how to get ...
4
votes
2answers
73 views

Specify rules for 2D cellular automaton?

If I want my rule to affect cells in this way: dead $\to$ dead $\iff$ Cell has $n$ living neighbours, $n\in A$ dead $\to$ alive$\iff$ Cell has $n$ living neighbours, $n\in B$ alive $\to$ dead $\iff$ ...
1
vote
1answer
50 views

RulePlot but with integers instead of colors?

I would like to produce something like the output of a RulePlot for a CellularAutomaton, but where the output state is an ...
5
votes
2answers
94 views

How to run a CellularAutomaton until a configuration is repeated?

I would like to do something like CellularAutomaton[10, {1, 0, 0, 0, 0}, 2^5], but instead of running for 2^5 steps, it should ...
2
votes
2answers
52 views

How to Update a Finite-Width Cellular Automaton

How does one instruct CellularAutomaton to wrap at the edges? (I want a 2d finite-width CA, so it evolves on a torus.) I cannot tell from the docs if this is ...
5
votes
2answers
136 views

Improve “Game of Life” on a mosaic

I had the idea of generalizing Conways Game of Life from a regular lattice to act on a Poisson Voronoi mosaic (tessellation). The code below works but is maybe not the best idea in terms of speed. I'...
1
vote
0answers
47 views

Looking for a way to run through every time step of a cellular automaton function with random seeds

I have been creating 2D cellular automaton functions in Mathematica and I would like the output to be a graphical representation of the array at each time step. I know I can do this with ListAnimate: ...
0
votes
0answers
39 views

Creating a 3D version of the rule 90 cellular automaton

I need help. I want to create a 3D version of the rule 90 cellular automaton, but I don't know how to do it. Please help me. It is for a class in the theory of chaos. this is my code ...
34
votes
1answer
679 views

Searching for still lifes in Conway's Game of Life

I'm trying to search for still lifes in Conway's Game of Life. An object in Conway's Game of Life can be represented by an array of booleans, say, Array[b, {w, h}]....
9
votes
3answers
413 views

Approximating Voronoi diagram without any distance checks

When reading the Wikipedia article on Voronoi diagrams I was fascinated by this animation: https://en.wikipedia.org/wiki/Voronoi_diagram#/media/File:Voronoi_growth_euclidean.gif I noticed that to ...
7
votes
1answer
295 views

How to calculate CellularAutomaton rule numbers in higher dimensions?

Where can I find documentation of the rule number convention for CellularAutomaton for higher than 1 dimension? I understand the convention for elementary 1D ...
2
votes
0answers
120 views

Weights in Cellular Automaton

It is not clear for me how are the weights used in the function CellularAutomaton. The code for outer totalistic 1D CA is: $$\bf{OT}= \sum_{i=0}^{2r(k-1)} \sum_{j=0}^{k-1} k^{k i+j} \phi_{out-tot}(j,...
4
votes
2answers
354 views

Custom Cellular Automata rule with k colors

How can I use the CellularAutomaton function to create a 2D automaton using a custom function and k colors? I understood from this post how to use custom rules for 1D automata. I'm trying now to do ...
5
votes
2answers
142 views

CellularAutomaton's Plot Range

I want to control the plot range of CellularAutomaton to show both left and right sides when using rule 60. Currently I have this: But I want to have something ...
1
vote
0answers
68 views

Generalization of DiscreteMarkovProcess?

I am trying to create a Markov chain using the initial state of a probabilistic cellular automaton, that is a list of length 8, as the first argument of the function ...
11
votes
3answers
818 views

Converting Game of Life images to lists

I want to convert images of GoL configurations into binary matrices to run in Mathematica's CellularAutomaton. I know that there's a collection of GoL patterns in ...
14
votes
1answer
311 views

Implementing the Biham–Middleton–Levine traffic model as CellularAutomaton

In an attempt to understand how to make rules for CellularAutomaton[], I set out to try to implement the Biham–Middleton–Levine traffic model. It is a 2D, ...
8
votes
1answer
627 views

Notation for 2D, semitotalistic, 9-neighbor Moore cellular automata

I am trying to run the semitotalistic rule B45678/S5678 on a torus, I found a program that runs game of life (B3/S23): ...
2
votes
0answers
65 views

Cellular automaton to map one vector to another in a special way [closed]

I have 2 vectors: Vector J of dimensionality N Vector K of dimensionality M M >> N by order(s) of magnitude. I need to find a cellular automaton G: K -> G -> J G however needs to be such that ...
3
votes
2answers
62 views

Setting initial conditions of a domain grid?

So I'm writing some code to try and produce a cellular automaton which will model an oscillatory chemical reaction, but I'm trying to set up the initial conditions of the grid so that I can vary them ...
4
votes
1answer
257 views

Computing Reversible CA with CellularAutomaton

This computes and plots 127 steps of the evolution of 150R (the reversible version of rule 150). ...
1
vote
0answers
69 views

How to create a cylinder with where the walls represent the output of a cellular automaton [duplicate]

So i'm trying to do this implementation of cellular automaton which replicates some random patterns generated by 3D printers like the ones below. I'd basically like to create a model which looks ...
3
votes
0answers
108 views

Issues reproducing reversible CA from NKS

I want to recreate the output of the reversible cellular automaton described in this page of the NKS book. The book specifies that this is a modified version of R214, where the new state (step+1) is ...
4
votes
1answer
190 views

Modifying Game of Life code so that the lattice can be seeded with life forms

I want to modify Game of Life code so that the lattice can be seeded with one or two new life forms like: ...
5
votes
3answers
638 views

Graph Coloring based on neighboring vertices? Cellular Automata

I would like to apply a majority rule cellular automata to graphs. Specifically, I would like to take a graph as input, and then define two functions, InitialColoring[graph] and MajorityRule[graph]. ...
3
votes
1answer
191 views

Using ParallelMap to run multiple Game of Life simulations simultaniously

My Assignment and Code As an exercise in Parallel computing I've been tasked with implementing Conway's GoL in a way such that at every iteration only a fraction of cells are updated. I'm then to run ...
4
votes
1answer
411 views

Cellular Automata Neighborhood as Node connections

Can I use the CellularAutomation[] function where the neighborhood is defined by the connections between nodes? For example, if 1 -> 2, 1 -> 3, 1 -> 8, 1 ->1, then the neighborhood of node 1 is the ...
7
votes
1answer
2k views

Game of Life in 3D

Is there a three-dimensional cellular automaton that in some sense generalizes Conway's Game of Life? If so, how might we use the CellularAutomaton command to ...
0
votes
2answers
814 views

2D Cellular Automaton: Initial conditions

I'm trying to write in Mathematica for a 20x20 grid, with 100 colours, with 4 neighbours. I want the initial conditions to be a 20x20 matrix consisting mainly of zeros. ...
3
votes
2answers
443 views

What does rule 30 mean in this example? [closed]

This starts with the list given, then evolves rule 30 for four steps. ...
11
votes
2answers
2k views

Can you apply the Cellular Automata function to a grid containing numbers?

Im attempting to simulate a simple evacuation model using cellular automata theory.My study aims to determine whether Cellular Automata can effectively represent how people would behave in a fire ...
8
votes
2answers
234 views

Is it possible to find a CellularAutomaton behind a sequence of 2D Tables

Maybe this is a hard question, maybe not. Whoever knows the answer can help me a lot starting working on CA theory. Let's suppose I have a sequence ...
2
votes
1answer
255 views

A Sierpinski-ish structure, via 2D automata

The project is originally based on a puzzle proposed by EIORU at http://www.ptt.cc/bbs/puzzle/M.1342451949.A.00F.html (若您懂得讀中文 / if anyone happen to read Chinese^^) last July. The descriptions, ...
2
votes
0answers
839 views

Is it possible to extract the rules of cellular automata as Mathematica code?

I would like to run cellular automata in the vertical direction if row index is greater than column index and in the horizontal direction if row index is less than column index, in a square array ...
8
votes
2answers
473 views

Use of Cellular Automaton or Discrete Convolution to calculate Potts Energy of a 2D Matrix

In a project of Monte Carlo Modelling of Grain Growth (Link) one of the most costly subroutines is the calculation of the Potts-Energy of an Monte Carlo Grid cell by comparing the center cell value ...
4
votes
1answer
1k views

How can I forecast time series data with cellular automata?

I have a time series data, for example data = FinancialData["JK:ADRO", "July 16 2012"] Can I use CellularAutomaton to ...
8
votes
2answers
1k views

Implementation of a new Game of Life Rule

I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action. I would like to implement the ...