# Questions tagged [cellular-automata]

For questions on cellular automata, a discrete model consisting of a regular grid of cells.

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### Using the rule stated below, is there a way I can plant trees on a 2D plane such that there are no trees in the first k diagonals? [duplicate]

This question was part of the problem set for PROMYS Europe 2020, a maths (or math, just in case I made anyone unhappy) camp held at Oxford every year. It was the one which I couldn't do, and I am ...
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### How to create a non-square 2D grid with spherical topology.

When programming Conway's Game of life on my computer. A problem arises; how to deal with the borders on the board? Do the cells at the border have to take into consideration less neighbours than the ...
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### is it possible to embed a fractal inside another fractal

I have been looking at one-dimensional (1D) cellular automata (CAs) which generate two-dimensional (2D) fractal patterns. Among the 256 1D elementary CAs, I tried to list down the fractal generating ...
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### Any good reference for start in Cellular Automata?

The question is as simple as the title. I want to know more about Cellular Automata, and his applications in Chemistry and Biology. I have read that, maybe, there is a relation of the topic with Graph ...
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### How to show that the probability that $\mathbb{Z}^d$ is internally spanned is equal to 1? (bootstrap percolation)

Presentation of the model: we consider the regular lattice created from $\mathbb{Z}^d$. At $t=0$, each site is said "active" independently with a probability $p$, "inactive" otherwise. At $t$, if a ...
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### Are there injective maps from a higher- to a lower-dimensional cellular automaton?

Suppose we have a cellular automaton on $\mathbb Z^n$ with cell values in the finite set $V$, with update function $u : V^{\mathbb Z^n} \to V^{\mathbb Z^n}$, and similarly another cellular automaton ...
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### Chaos in discrete space and time systems. Definition, tests, etc?

I have been working with a cellular automata model and have been struggling to characterize its dynamics. It seems to be displaying aperiodic behaviour in a certain part of the parameter space, but I ...
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### Expanding Nebula: Problem in Cellular Automata or Coding Theory

First post to Math Stackexchange. Recently I was posed with a mathematically intensive computer programming challenge that I am completely at a loss for solving. To give you some info on my math ...