# Tagged Questions

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### Calculate Density of Values in Cellular Automata

I am working with a special cellular automata that uses hexagonal cells rather than square cells, a hexagonal grid, rather than a square grid, and the set of complex numbers, rather than a finite set, ...
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### What counts as a “Neighbor” in Conways' game of life?

I have looked everywhere but I cannot find an answer for this. Since I am bored, I am trying to create this game, but I can't seem to figure out what is considered a "Neighbor". Is it only directly ...
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### What is an automata network?

I've tried Wikipedia and Google as first steps, but while I've found some interesting papers and articles, and a couple expensive textbooks, I've yet to find a clear definition of an automata network ...
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### Give a regular expression

Let Σ be {0, 1} Give a regular expression generating words over Σ containing an even number of 1’s or with a length which is multiple of 3. i came up with this solution: ε ( ((0*(10*10*)) + ((0+1) (...
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### 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 ...
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### Preventing cars from leaving a crossroad in a cellular automata traffic simulation

I'm writing a traffic simulation using cellular automata based on this paper It states that the rule in the middle of the crossroad always stays the same (184), but that the cell after the crossroad ...
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### Is there a possibility to determine/ estimate the topological entropy?

By $E$, denote the set of excited states $E=\left\{1,2,\ldots,e\right\}$ and by $R$ the set of refractory states $R=\left\{e+1,e+2,\ldots,e+r\right\}$. By $0$, denote the equilibrium state. The ...
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### Plotting the fundamental diagram of traffic flow

I have a traffic simulation and I don't understand how I can plot the fundamental diagram (flow rate vs density). I simulate the traffic as follows: I have a matrix that has as many columns as the ...
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### Why does this cellular automaton generate circular patterns?

I made a kind of cellular automaton game with the following rules. Each cell in a rectangular grid has a "water level" (a 32-bit floating-point number). In the next generation, water "flows" from each ...
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### Cellular automata orphan

Suppose we have 2-dimensional automata, with local rule(Moore neighbourhood): 0 if $a+b+c+d+f+e+g+h+i \leq 4$ 1 if $a+b+c+d+f+e+g+h+i \geq 5$ How to find orphan?
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### Free Gliders for Everyone?

According to Feynman's Lecture on Computation (Problem 5.1, p. 148 ) you can extract $E=kTN\log 2$ out of two copies of a random $N$ bit random tape. From this we can conclude that it takes the same ...
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### Elementary Cellular Automata Rule 232

Rule 232 can be expresses as: $c_n=1$, iff $c_{n-1}+c_n+c_{n+1}\geq2$ {$c_n=0$ otherwise) Figured out its Wolfram number(rule), that would be as mentioned in topic - 232 Here is link for cloud....
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### Asynchronous XOR cellular automata and complexity

I've been experimenting a bit with what I think is the simplest possible CA-like rule that generates complex patterns and behaviors: https://eloquence.github.io/elixor/ Essentially, I define an ...
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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 ...
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### Alphabets of Turing Machine

I'm not completely sure about equivalence of two definitions of Turing machine. The first one states that Turing machine has a finite alphabet $\Sigma$, set of states and some rules. Turing machine ...
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### How long before the prey can escape?

I've (sort of) come across the following problem in my research. The actual scenario is a little abstract to explain, so I'm rephrasing the problem in terms of a predator/prey scenario. I'm tagging ...
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### Is there a theory for cellular automata propagating signals in straight lines?

Is there a theory explaining how a cellular automata can propagate signals in straight lines? For example, this video shows how some "signals" travel down at a diagonal, even though they are composed ...
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### Watrous’s definition of Quantum Cellular Automata

I need some help understanding the second-to-last and final equations of the introduction to quantum cellular automata included below. My specific questions: What does it mean when the capital Pi ...
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### Conway's Game OF Life maximum periods on a set x by x game board.

I have taken interest in Conway's Game of Life and want to know if you guys can help me with a mathematical problem :) That is what this website is for right? You need to be familiar with the rules ...
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### online courses and books covering the theory of cellular automata

i would like to learn the theory cellular automata and know more about the research being done in this field and the links with other related fields such as artificial inteligence, computabilty and ...
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### What do 2-dimensional cellular automata rules actually mean?

There is a certain 2d cellular automata I am particularly interested in. It is called "rule 52928". It's used by Wolfram | Alpha on the loading screen. But what exactly does the rule mean? Is it an ...
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### Why are the $T^{3n}\mu$ Bernoulli-shifts, too? Can you clarify this?

Preliminaries: Definition of Bernoulli-shift Let $X=\left\{0,1,2\right\}^{\mathbb{Z}^d}$ and $\mathcal{B}$ the Borel-$\sigma$-Algebra on it. Moreover, let $\mu_{p_0,p_1,p_2}$ denote a Bernoulli-...
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### Why does follow that $\eta_n\to 0$ in distribution as $n\to\infty$?

Following setting: Consider $\left\{0,1,2\right\}^{\mathbb{Z}}$. And on it the following dynamics: A site $x\in \mathbb{Z}$ represents a cell which can be 1, 2 or 0. A 1 becomes a 2 in the next time ...
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### Proof of the Curtis-Hedlund Theorem: Why is there a function $\mu\colon A^S\to A$ such that $\tau(x)(1_G)=\mu(x_{|S})$ for all $x\in A^G$?

Here is the Curtis-Hedlund Theorem and its proof [the sets $V(\cdot,\cdot)$ used in this proof are explained below.]: My problem is I am not sure that I have understand that correctly. So I ...
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### Is cellular automata something that is studied in mathematics departments?

I am interested in studying cellular automata but am unsure if I should be looking at CS or mathematics graduate departments. Symbolic dynamics seems to have some tie to cellular automata but I haven'...
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### Good data structure for hyperbolic tiling

Say you're doing something computational where each data point is a tile in a (not necessarily Euclidean) 2-dimensional tiling, for instance, a Life-like cellular automata. You might want a data ...
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### recursive automata, or recursion mod 2.

Consider the list of length $m$ $(1,0,\dots 0)$ we call this list $l_1$, we now define a sequence of lists recursively, where $l_1$ is the previous list, and if $l_n$ is the list $(a_1,a_2\dots a_n)$ ...
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### Have $3$-dimensional cellular automata been studied at all?

Recently, I have become interested in the Game of Life and other similar cellular automata. I notice how these cellular automata operate in a square tiling on $2$-space, and it seems as if similar ...
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### Writing in 1993, a researcher noted that it is hard to prove things about a cellular automata model - has this changed?

Leah Edelstein-Keshet in her 1993 article Cellular automata approaches to biological modelling writes: We do not believe that CA should be viewed as a replacement for rigorous mathematical models. ...
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### Rigid spaceships in Conway's Game of Life

(1) Is it true that there are no rigid spaceships in Conway's Game of Life, i.e. spaceships with period 1 i.e. spaceships of constant shape (only allowed to rotate) of non-zero translational velocity? ...
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### Are there cellular automata with “long range” rules?

Common cellular automata have rules that only check cells' immediate neighbours, in the current, immediate step. Have CA been explored that have rules that are "longer range" (spatially and temporally)...
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### Garden of Eden States in Cellular Automata

I am just beginning to study cellular automata and I am having trouble understanding the so called Garden of Eden states. How can a deterministic algorithm wind up in a state that has no pre-image, ...
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### Moore neighborhood on a two-dimensional Cartesian lattice

How many distinct cellular automata rules are there that use the Moore neighborhood on a two-dimensional Cartesian lattice if we allow three bits (eight states) per site?
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### 2 dimensional cellular automaton for prime twins?

Is there a 'simple' 2 dimensional cellular automaton to generate all prime twins ? With 'simple' I mean not too many states per cell and not so many rules. Thus a universal turing machine equivalent ...