For questions on cellular automata, a discrete model consisting of a regular grid of cells.
Questions tagged [cellular-automata]
155 questions
115
votes
7 answers
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
- 1,745
25
votes
1 answer
Golden Ratio appears in this Rule 30 variation?
The cellular automaton Rule 30 is most commonly explored starting with a single 1 cell against a background of infinitely many 0 cells. This gives the familiar plot:
However, if you start with a 1 cell but use a background consisting of the pattern…
Trevor
- 6,144
- 16
- 39
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
- 2,845
17
votes
1 answer
Is there a simple maximally general generalization of Noether's theorem to arbitrary dynamical systems?
Noether's theorem informally states something like "symmetries in the dynamical law imply conserved quantities". However, the theorem is generally stated in terms of physics-specific classes of dynamical systems such as Lagrangian or Hamiltonian…
user56834
- 12,323
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
- 403
16
votes
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
- 21,868
15
votes
3 answers
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
- 195
12
votes
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
- 661
11
votes
0 answers
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
- 111
11
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
- 32,728
10
votes
0 answers
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
- 201
9
votes
1 answer
Infected cubes puzzle in 3D with threshold 4
(Now cross-posted to Puzzling SE.)
3D infected cubes puzzle with threshold $4$:
On an $n\times n\times n$ cube, some cells are infected; if a cell shares a face with $4$ infected cells, it becomes infected. What's the minimum number of initially…
Akiva Weinberger
- 25,412
7
votes
0 answers
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
- 447
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7
votes
1 answer
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…
Christopher King
- 10,773
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
- 73