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.
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Using a one-dimensional Cellular Automaton to show states of each of the cells
Cellular Automata perform distributed computation through the iteration of
(relatively) simple logic within individual cells in an array. The following table defines the logic for a one-dimensional ...
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1answer
68 views
Is it there any computer/cellular automaton/brain to compute logically impossible and incomputable things? [closed]
Is it there any computer or cellular automaton or model of the brain where they could compute logically impossible things and incomputable things?
For example, if we wanted to compute/simulate/think ...
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Generalization of Parallel Computing Architectures, Multi-Agent Architectures, and Cellular Automata
This question is for resource or explanation generalizing or simplifying the ideas of parallel computers, cellular automata, and multi-agent architectures. I am interested in the requirements for ...
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Cellular automata for 2d cloud simulation
I want to build a cellular automata that simulates a behaviour that looks like clouds, that is: infinite and random cycles, pieces can gather or break apart, just like the image below:
My question is:...
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Is it possible to simulate oracle machines on 1-dimensional cellular automata?
My instinctual response is that it is possible, but I can't see how to simulate the oracle tape on a 1-d CA.
If not, are they able to be simulated on n-dimensional CA? My thought is that the oracle ...
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22 views
Pairing as opposed to cellular automata
The rule is that an isolated lit square in a grid of squares must be paired in the x-direction (either immed. left or right of it) AND y-direction. That is, from surrounding cells, the closest lit or ...
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In what sense can a cellular automaton be Turing complete? [duplicate]
The rule 110 cellular automaton is known (or claimed) to be Turing complete. But what exactly does it mean?
I do know what Turing completeness mean. Roughly speaking a language is Turing complete if ...
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1answer
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Algorithm to estimate the probability that a “0 and 1 matrix” fills up following the bootstrap percolation rules
Presentation of the model: we consider the regular lattice created from $\mathbb{Z}^2$ (It's no more, no less a square lattice).
At $t=0$, each site is said "active" independently with a probability $...
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1answer
182 views
How 2d cellular automata rules works?
How 2D Cellular Automata rules sequences works?
For example, in elementary cellular automata, when we look at the binary sequence of the rule number, we understand that first bit says if all neighbors ...
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1answer
59 views
Classes of outer totalistic cellular automata
I'm wondering if anyone knows of any place where the Wolfram classifications of many outer totalistic cellular automata have been catalogued. The classes of a few examples are given in A New Kind of ...
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1answer
715 views
Turing-completeness, Conway's Game of Life and Logical Gates
I was recently given an assignment at university asking me to discuss the universal computational capability of Conway's Game of Life.
I'm not required to actually build up a Universal Turing machine ...
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25 views
Binary arrays for cellular automata
Where can I download some interesting cellular arrays for Conway's Game of Life? Arrays such as the Gosper glider gun, etc? I can find the images easily enough, but are they available somewhere in ...
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1answer
38 views
Need introductory guide to cellular automata for geographic automata systems
I would like to work on urbanisation and I've read that cellular automata has potential use on model urban sprawl. However I need some kind of introductory to cellular automata in order to tackle an ...
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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 ...
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1answer
67 views
Simple elementary cellular automata with high period?
I'm looking for a simple rewrite system which displays high period.
In order to do that, I've ran a brute-force search on every elementary cellular automata, for a few fixed memory lengths ...
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1answer
21 views
How to identify strongly confluent cellular automatas?
Lets represent a class of cellular automata as a finite, unidimensional bit array state : [Bit], plus a rewrite rule ...
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1answer
46 views
Is there any count-preserving cellular automata which tends do “10101010…”?
Suppose that I have a bit string of finite length. Is there any bit rewriting rule rewrire :: (Bit,Bit,Bit) -> (Bit,Bit,Bit), that doesn't change the total count ...
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1answer
91 views
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 ...
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1answer
185 views
Complexity of $n \times \log n$ tiling problem
Is there a polynomial time algorithm for an $n \times \log n$ tiling problem?
For instance: Suppose $A$ is a finite alphabet. A tile is a $2 \times 2$ matrix of elements from $A$. A tiling is a ...
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1answer
378 views
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 $i$. ...
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2answers
129 views
Consistent Simulation of Cellular Automata on Infinite Grid
Let's say that you have an infinite grid of cells.
A program is run per cell, where you have read access to some finite number of cells (for the previous state in time), but you only have write ...
5
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1answer
248 views
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. ...
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1answer
91 views
Are Cellular Automata always computers?
I was reading on Complex Systems journal and found a paper where the author states that a cellular automaton can be viewed as a computer.
In the introduction part:
Cellular automata can be viewed ...
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1answer
118 views
Why some rules in Elementary Cellular Automata halt and others don't?
I was looking over stephen wolfram's work mainly about Elementary Cellular Automata, i see that for all rules with N steps {i.e 200 steps} they show the same pattern {i,e rule 90 running on 20 steps ...
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1answer
41 views
Is there a similar categorization to Elementary Cellular Automata?
Elementary cellular automata show different systems and fractals like rule 30, rule 90, and rule 110. I want to know if there is another classification or type which shows similar structures just like ...
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1answer
36 views
What is the relation between universality and chaotic behavior in Elementary Cellular Automata?
So i know that rule 110 from Elementary Cellular Automata is universal but i am wondering if we had other chaotic behaviors let's say there exists a system that shows nearly infinite chaotic behaviors ...
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1answer
689 views
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 ...
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1answer
96 views
What is the relation between pure mathematics, applied mathematics and Cellular Automata?
I was reading about pure mathematics and I am wondering if there is a relation between it and Cellular Automata.
Broadly speaking, pure mathematics is mathematics that studies entirely abstract ...
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0answers
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What is the relation between Universality and simulations of Cellular Automata structures?
Elementary Cellular Automata and Conway's Game of Life show interesting Cellular structures, suppose we have a computational model {a Cellular Auotmaton} that can simulate both CA types (ECA & ...
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2answers
85 views
How Cellular Automata is related to Automata Theory?
I have read about Automata Theory where it is about the study of abstract machines and automata.
And i know that an abstract machine takes the input, process it and create the output, just like ...
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0answers
37 views
What is the relation between Universality and Geometric shapes in cellular automata?
When wolfram described Elementary Cellular Automata, most of the rules appeared as triangle and lines.
Now, Rule 110 consists of triangles which is proved to be universal.
Is there a relation ...
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2answers
250 views
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 ...
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1answer
292 views
Does solving mathematical equations with Cellular Automata structures means it is universal?
I'm working on a research about Elementary Cellular Automata (ECA), and i found a method to build a system that can solve mathematical equations by using a specific cellular automaton structure.
The ...
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1answer
75 views
Can a cellular automata structure simulates another cellular automata structure?
In Elementary Cellular Automata, rules can show one pattern, but i am wondering if there is something where a cellular automata structure can simulate another structure?
Is there a category for this ...
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2answers
278 views
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 ...
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3answers
297 views
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 ...
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Immutable data structures for 2d+ lattices
I would like to find an immutable/persistent data structure that allows efficient updating for 2d (or higher) lattices/arrays/matrices, and reasonable performance when appending in any direction. ...
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1answer
73 views
Which cellular automata rules are suitable for randomizing an input sequence?
S. Wolfram has in has book "A New Kind of Science" listed 256 simple rules of cellular automata. Which of these rules could via iteration essentially contribute to render an input sequence more random ...
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2answers
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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 ...
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1answer
79 views
How to synchronize a 2d cellular automaton in $\Theta(\sqrt{n} \log n)$ steps
Let's assume we have given a two dimensional cellular automaton with an initial configuration where alls cells are in an quiescent state, expect for one square of cells. Let $n$ be the number of cells ...
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0answers
411 views
How to simulate a cellular automaton via a Turing machine
It is rather easy to see that every cellular automaton can be simulated by a Turing machine: We can simulate a cellular automaton with an appropriate C program and every C program can be simulated by ...
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1answer
69 views
Cellular Automata Using Small Boards
I'm working on making patterns for a digital lava lamp (essentially, making interesting patterns using a 4x10 grid), and I've been looking into cellular automata. I tried implementing some variations ...
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3answers
359 views
What is the distribution of Garden of Eden patterns in cellular automata with increasing pattern size?
In a given cellular automaton, such as Conway's Game of Life, is there anything known about how many Garden of Eden patterns there are by pattern size? Say, pattern size is n x n, what's the ...
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2answers
87 views
Does the state of a cell in cellular automata has to be from a finite set?
In most (all I have seen) work on cellular automata, the state of a cell is from a finite set. Such as a cell can take value from a binary set, or from among few colors. Can we define the state to be ...
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0answers
158 views
Time Complexity of Simulating CA with TM
This question is a follow up to the question: Proving Equivalence of 1-dimensional Cellular Automaton and Turing Machines.
To simulate a CA with a TM, I used a construction which placed a marker on ...
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1answer
643 views
Proving Equivalence of 1-dimensional Cellular Automaton and Turing Machines
I'm considering an automaton $A$ over a alphabet $\Sigma$, with a set of states $Q$, such that $\Sigma \subset Q$, which includes special "accept" and "blank" states not in $\Sigma$. It also has an ...
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2answers
284 views
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 ...
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1answer
540 views
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?
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2answers
120 views
How does an automaton actually “compute”?
In my studies in computability I have come across the notion of the "machine", an abstract representation of a device that essentially computes. I have read about Turing Machines and Wolfram's binary ...
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2answers
5k views
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, ...
