For questions on cellular automata, a discrete model consisting of a regular grid of cells.
Questions tagged [cellular-automata]
142 questions
2
votes
3 answers
In the linked image, why does a pattern form, as opposed to random noise?
Image in question
This image was generated line by line, with each pixel's value determined by a set of rules:
If the pixel is on the edge, set to the same color as the previous pixel 1 away from the edge
If the left and right pixels on the…
Nick Engle
- 21
2
votes
0 answers
Asynchronous XOR cellular automata and complexity
I've been experimenting a bit with what I think is the simplest possible CA-like rule that generates complex patterns and behaviors:
https://eloquence.github.io/elixor/
Essentially, I define an array of size, then walk it in either direction, and…
Eloquence
- 21
1
vote
0 answers
What are the various types of rules / rule systems created or commonly used for studying 2D cellular automata?
I am working on implementing a cellular automata framework in JavaScript, though I don't really have a good sense of what I'm doing yet. I have spent days searching for "rules" for cellular automata, but didn't really find much in terms of…
Lance
- 3,698
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0 answers
Maximum generations possible for any initial configuration on a Conway GOL Torus
Game of Life (GOL) is well known. I will not try to describe it myself. More details here: https://conwaylife.com/wiki/Conway%27s_Game_of_Life
A Conway GOL Torus is a variation of GOL where the board wraps around (ie the number of cells are finite).…
Mircea
- 111
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vote
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Are there impossible patterns in Conway's game of life?
Given a grid representing a state in Conway's game of life, if there is no pattern that leads to this state, this means that there exists a forbidden $N\times N$ pattern for some $N$.
If so what is the smallest $N$ such that an $N\times N$ pattern…
zooby
- 4,343
1
vote
1 answer
Cyclic cellular automaton with 3-neighborhood
Consider a 2D cyclic cellular automaton with randomized starting states and the
usual von Neumann 4-neighborhood ruleset. It is well-known that this CA
produces a stable and periodic state after a few hundred iterations. Yet
removing just one…
Ali Kwant
- 91
1
vote
1 answer
Is there any 3D patterns, if we are to stack up each generation of "Conway's game of life" on top of each other?
1D Cellular Automata do not show any interesting patterns if we look at each state only one at a time in Succession, but if we put each state below each other, we can see patterns emerging.
In the case of 2D CA like Game of life , we can see…
1
vote
1 answer
How does On/Off Reversal work in Life-Like Cellular Automata
I've recently been made aware of the concept of on-off rule reversal in life-like cellular automata. I understand the algorithm for calculating the rule reversal from a given rule. But I don't understand why the algorithm is the way that it is, or…
brubsby
- 270
1
vote
1 answer
Finding Life-Like Cellular Automata Rules and Initial States with Guaranteed Still End States
My goal is to find all rulesets of life-like cellular automata and initial states that, when simulated in a toroidal grid (although non-toroidal would be interesting as well) of arbitrary finite dimensions, eventually end up in a fixed end state…
brubsby
- 270
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vote
1 answer
How do I find the rule number for a cellular automata rule?
I have been given a rule for a cellular automata (in which so long as one adjacent cell is living but not both the next generation lives), but I can't find any reference works on cellular automata rule numbers.
hamilton.julius
- 123
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vote
0 answers
What mathematical concept captures the idea of a one-way or unidirectional space or operation?
There are lots of places where we encounter one-way operations where there is a defined way "forward" but no way to really go "backwards". I can think of a number of examples but the so called "arrow of time" is what really got me thinking about…
nickdmax
- 111
1
vote
1 answer
What do 2-dimensional cellular automata rules actually mean?
There is a certain 2d cellular automata I am particularly interested in. It is called "rule 52928". It's used by Wolfram | Alpha on the loading screen.
But what exactly does the rule mean? Is it an analog to the rules for elementary cellular…
Daniel
- 1,335
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1 answer
Trouble understanding proof in "Aperiodicity in One-Dimensional Cellular Automata" paper by Erica Jen
From the proof of page 7 in https://digital.library.unt.edu/ark:/67531/metadc1443182/m2/1/high_res_d/7230855.pdf (page 10 of the PDF):
The fact that $R$ is injective in its $(i+1)$-th component (the “mirror”’ argument holds for injectivity on the…
brunni
- 53
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votes
0 answers
How to interpret wolfram rule 108 as a simplified populationmodel
I have made a Matlab-program as to iterate wolfram-rule 108 on any chosen begin situation. However my question is how this rule can be interpreted as a simplified version of a population model.
(some graphs for rule 108 can be found here :…
Michelle_B
- 415
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2 answers
online courses and books covering the theory of cellular automata
i would like to learn the theory cellular automata and know more about the research being done in this field and the links with other related fields such as artificial inteligence, computabilty and language theory.
Any recommended books and online…
ceillac
- 113