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0answers
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Langton's ant questions

I'm a mathematician currently working on the Langton's ant conjecture, just for fun. I have some result but I don't know if they are meaningless. So that is why I'm asking. 1) Is there a mathematical ...
2
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0answers
94 views

A variant of the tiling problem

A classic tiling problem with Wang tiles has the form: Given $n$ tiles $T=\{t_1,...,t_n\}$ and some constraints $H,V\subseteq T\times T$, is there a way to tile a $w\times h$ rectangular grid with $...
1
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1answer
43 views

Data Mining of self-replicators

My current (very limited) understanding of the creative process that leads to the design of self-replicators is that any particular self-replicator, like Universal Constructor, Langton's loop or ...
8
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5answers
348 views

Are there any schools with researchers interested in cellular automata?

I have been working on an independant project focusing on cellular automata and was wondering if this might be something that I could continue on in graduate school somewhere. I've seen some ...
0
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1answer
131 views

Where is the proof of universality of Rule110 in Stephen Wolfram's book?

I have Stephen Wolfram's book A New Kind Of Science. And I want to find the proof of the universality of Rule 110. I couldn't find the clue in the contents page since it only shows 12 chapters and no ...
3
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0answers
149 views

Meta Game of Life

Apparently, Game of Life has been implemented in Game of Life. For example: https://www.youtube.com/watch?v=xP5-iIeKXE8 The device used here is called the "OTCA Metapixel", and supports all life-...
1
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0answers
99 views

Finding a cellular automaton that reproduces a finite-sized spacetime patch with reduced coloration

Note: This question is an extension of: Computational complexity of finding a (1D deterministic) CA that achieves a desired spacetime history "patch" after $t$ iterations, which Marzio De ...
2
votes
1answer
140 views

Computational complexity of finding a (1D deterministic) CA that achieves a desired spacetime history “patch” after $t$ iterations

Question description: Consider the problem of finding a minimum $n$-color $k$-state one-dimensional cellular automata (minimizing $k$ for some fixed value of $n$ or vice versa), with communication ...
28
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4answers
3k views

Does a noisy version of Conway's game of life support universal computation?

Quoting Wikipedia, "[Conway's Game of Life] has the power of a universal Turing machine: that is, anything that can be computed algorithmically can be computed within Conway's Game of Life." Do such ...
2
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1answer
592 views

Langton's ant highway conjecture and undecidability

I was recently reading about Langton's ant and the related conjecture which states that for every initial configuration, the ant eventually starts building a 'highway'. I also read that it has been ...
-3
votes
1answer
413 views

Minimal Turing Machine implementation / Von Neumann UC [closed]

I've written a small python program which implements a Turing Machine with a finite tape. It has a tape, a head, a state register and a set of transfer functions ("the program"). The difference to a ...
2
votes
2answers
281 views

Difference between Stencil -structures and Cellular Automata Category-theoretically?

Definitions Stencil = "For a given point, a stencil is a pre-determined set of nearest neighbors (possibly including itself)." (source) Wikipedia's definition (source) = It looks ...
2
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1answer
740 views

Initial conditions for universal Rule 110

In A New Kind of Science, Wolfram proves that the Rule 110 cellular automaton can emulate a cyclic tag system, and is therefore a universal computer. I was wondering what specific initial conditions ...
2
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0answers
173 views

Particle collisions for universal computation

Proof of universality of Game of Life is straightforward (CAFAQ): (two annihilating glider streams with gaps (ie. 0s) are colliding, one is "data" and the second is all glider filled, ie.: 111111....
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0answers
133 views

Density of black cells in rule 110 cellular automata [closed]

Is there a way to compute the limit of the ratio (number of black cells)/(number of white cells), in the rule 110 or rule 30 automaton? With initial state = 1 black cell. Simulation of first 120000 ...
4
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1answer
325 views

Quantum cellular automata

This questions is cross-posted from MathOverflow A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use ...
5
votes
2answers
479 views

Isolation in Turing-complete reversible cellular automata

I don't know much about the terminology and the results on cellular automata, but I would like to ask a question about an conjecture I thought. Consider Turing-complete reversible cellular automata. ...
6
votes
1answer
346 views

On 1-dimensional cellular automata

I'm interested in linear 2-state cellular automata (with local rules only) that could compute the majority function. Say the state of a cell is either 0 or 1. Is it possible to have a cellular ...
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0answers
987 views

Can a Penrose tile cellular automaton be Turing-complete?

This question was based on an incorrect premise ... see Colin's comment below. Forget it. This was inspired by the discussion on this Math Overflow question. First, I need to define our terms. In a ...