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Questions tagged [cellular-automata]

A computational model composed of a grid of stateful cells and a set of rules describing when to change a cell's state.

A cellular automaton (CA) is a discrete model of computation consisting of a finite-dimensional grid of stateful cells, a finite set of states, and a fixed function that relates the state of a cell at time $t$ to the state of a cell's neighborhood at time $(t-1)$.

Questions tagged with cellular-automata typically examine some property of CAs, specific CA rule sets, or the relationship of cellular automata to other models of computation.

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How is the rule 110 Turing complete?

I've read the wikipedia page for rule 110 in cellular automata, and I more or less know how they work (a set of rules decides where to draw the next 1 or 0). I've just read they're Turing complete, but I can't even fathom how would you 'program' in…
AncientSwordRage
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Are today's massive parallel processing units able to run cellular automata efficiently?

I wonder whether the massively parallel computation units provided in graphic cards nowadays (one that is programmable in OpenCL, for example) are good enough to simulate 1D cellular automata (or maybe 2D cellular automata?) efficiently. If we…
Stéphane Gimenez
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Cell walls in Conway's Game of Life?

Do there exist robust structures in Conway's Game of Life? For instance, has anyone constructed a spaceship with a shield that absorbs all small oscillators and gliders it collides with?
Nick
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1/r attractive force by cellular automaton

Does there exist a cellular automaton (in 2D) which simulates a $1/r$ force between particles? More specifically, I would like to know whether it is possible, with strictly local update rules, to have two objects (defined within the model) attract…
MJK
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Is the halting problem decidable for 3 symbol one dimensional cellular automata?

I've been trying to figure out if the halting problem is decidable for 3-symbol one-dimensional cellular automata. Definition Let $f(w,i)$ denote the configuration of the system at time step $i$. More formally $f:A^*\times \mathbb{N} \to A^*$, where…
Pavel
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Influence of the dimension of cellular automata on complexity classes

Let's take as an example the 3d → 2d reduction: What's the cost of simulating a 3d cellular automaton by a 2d cellular automaton? Here is a bunch of more specific questions: What kind of algorithms will have their time complexity changed, by how…
Stéphane Gimenez
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Is there any field that studies the equivalent of cellular automata, but for arbitrary graphs rather than 1D cells?

A cellular automaton consists of a sequence of cells, each with a state, and a globally symmetric transition rule based on the neighbors of a cell. They can be interpreted as graphs where each cell is a node, and each node has an edge to a…
MaiaVictor
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What is the difference between computational model, model of computation and a computer?

I was browsing the forum where i came by this question, it says that rule 110 from {ECA} is a computation model. What is the difference between a computation model and model of computation and how can we relate them to computers ? A model of…
Aron Anothony
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How to prove universality in complex systems?

I'm working on my graduation project for CS, which is about cellular automata. Recently, i was able to build a system where the input is transferred to multiple different structures at once. The input consists of numbers, a sequence of numbers…
Harith Eltim
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Are Elementary Cellular Automata structures considered to be fractals?

I know that a fractal is a non ending pattern, like Pascal's triangle or Sierpinski's triangle, which are the same as Rule 90 from Elementary Cellular Automata. But, what about the other rules from Elementary CA? Are they also considered to be…
jason
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Is the number of inequivalent elementary cellular automata rules really 88?

Everywhere from Wolfram's "New Kind of Science" (p. 57) to Wikipedia they say that, out of all possible 256 (=2^8) elementary cellular automata rules, 88 are inequivalent (as defined in the Wikipedia article). Now, the problem is that I am failing…
Vilius Normantas
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What does Cellular Automata Pre-image problem actually means?

I am reading about Cellular Automata and Computational Complexity and i found a related paper by F. Green, NP-Complete Problems in Cellular Automata. In the 2nd page he lists three NP-Complete problems related to CA, the first problem is: CA…
Henry akpo
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How rule 110 would be proven to be universal if the tag system did not exist?

I was reading about Cellular Automata and I read in this question that Matthew Cook proved that rule 110 is universal, and that his proof relied upon showing how rule 110 can simulate a tag system. Is there another method or information that would…
Henry akpo
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Are deterministic and nondeterministic Cellular Automata equivalent?

It seems that in CA context nondeterministic (ND) means probabilistic, not ND as in NFSMs. At least I haven't seen a paper or book which discusses NCAs, without talking about probabilistic CAs. I haven't even found a definition anywhere. It feels…
rtur
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Complexity of still life extentions in Game of Life

The game of life is one of the most famous cellular automata in 2D. It has a variety of objects, some of them are moving like gliders, some have an oscillating behavior and others do not change at all, i.e. are still lives. I am interested in the…
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