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

# Questions tagged [cellular-automata]

122 questions

**114**

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### Is black hole pattern possible in Conway's Game of Life that eats/clears everything?

Is black hole pattern possible in Conway's Game of Life that eats/clears the infinite universe plane ?
Formally, is there a pattern that satifies following requirements?
The pattern has finite size.
The universe plane has infinite size.
Each cell…

VainMan

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**18**

votes

**2**answers

### How to translate mathematical intuition into a rigorous proof?

I've seen a lot of questions about how to develop mathematical intuition, but often I have the opposite problem.
Several times I have run into a situation where I want to solve a math problem, and I play around with it until my intuition reaches the…

Riley

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**16**

votes

**2**answers

### Infection spread on a torus chessboard

In one of his books, Peter Winkler includes the following problem:
A disease is spreading on a $n\times n$ chessboard as follows: if a healthy cell is neighboring at least 2 infected cells, it becomes infected. Using the property that the perimeter…

user2471

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**16**

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**0**answers

### What turmite runs the longest before becoming predictable?

When looking at 2D Turing machines, many of them eventually become predictable. For example, Langton's Ant, the champion 2-color 1-state turmite, develops a highway after 10,000 steps. Predictable behavior includes Traps (as in Worm Trails),…

Ed Pegg

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**14**

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### Conway's Game of Life

Is there a mathematical way to directly calculate iteration n from the first iteration skipping calculating the iterations in between in Conway's Game of Life? I would assume, if it is possible, it would involve arrays.

The Diamante

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**11**

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**2**answers

### What is the maximum "alive density" of cells in Conway's Game of Life when played on a torus?

I've read that Conway's Game of Life (CGOL) can have unbounded growth from a finite initial number of alive cells (e.g. a glider gun). However, if CGOL is played on a torus, space (the number of cells) becomes finite, and glider guns are guaranteed…

Ron Shvartsman

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**11**

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### Fractal Pattern from Queen's Move Construction

This question relates to the OEIS sequence A279212.
Fill an array by antidiagonals upwards; in the top left cell enter $a(0)=1$; thereafter, in the $n$-th cell, enter the sum of the entries of those earlier cells that can be seen from that…

Alec Jones

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**10**

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### What is the expected length of the "Slimy Slug" cellular automata

A "Slimy Slug" is a simple probabilistic cellular automata defined as follows:
The Slimy Slug lives on an infinite, two-dimensional, white-coloured, square grid. For each iteration, the slug follows these rules:
Paint the cell the Slug is on…

MadScientist

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**10**

votes

**2**answers

### Irrational numbers generated by a deterministic cellular automaton?

If we consider a simple 1D cellular automaton (acting on a binary string) and record a value at a fixed position in the string, we can interpret the recorded sequence as a binary number.
Most simple deterministic cellular automata generate periodic…

Yuriy S

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**7**

votes

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### Does Day and Night on a Klein bottle have a steady state?

Place a $m \times n$ ($m,n \ge 3$) square grid on a Klein bottle. On each square, we select an arbitrary non-mirror symmetric marker, and arrange them on the Klein bottle in some way. This arrangement is called a "position".
Now, we introduce the…

PyRulez

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**7**

votes

**1**answer

### 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 background, I'm a senior physics major and computer…

Kyle

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**7**

votes

**2**answers

### How can I prove that Game of Life's evolution function is continuous?

Conway's Game of Life is a cellular automaton, but also a discrete dynamical system. In all the papers, books, notes I have read on it, it is never never never shown that its evolution function is continuous. I tried to show it myself, thinking it…

user386721

**6**

votes

**2**answers

### Can SAT instances be solved using cellular automata?

I'm a high school student, and I have to write a 4000-word research paper on mathematics (as part of the IB Diploma Programme). Among my potential topics were cellular automata and the Boolean satisfiability problem, but then I thought that maybe…

cosmicomic

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**6**

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### Noether's theorem in SmoothLife?

Conway's Game of Life, being discretized in both space and time domains, has no locally conserved quantities. SmoothLife, however, is a generalization of the Game of Life to a continuous and spatially-isotropic domain. The evolution rules of…

Logan R. Kearsley

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**6**

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### what are the practical uses of "game of life" or "langton's Ant"

A few questions:
Besides looking really cool, what are the practical uses of "game of life" or "langton's Ant"? I understand how agent-based modeling itself is a potentially useful methodoly, not how the 2D game-of-life representation is useful…

user60462

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