Cellular automaton - Cellular automata in the chemistry lab

A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory, mathematics, and theoretical biology. It consists of an infinite, regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at time t is a function of the states of a finite number of cells (called its neighborhood) at time t-1. These neighbors are a selection of cells relative to the spec ...

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• Cellular automaton - History of cellular automata
• Cellular automaton - The simplest cellular automata
• Cellular automaton - Reversible cellular automata
• Cellular automaton - Totalistic cellular automata
• Cellular automaton - Uses in cryptography
• Cellular automaton - Related automata
• Cellular automaton - Cellular automata in nature
• Cellular automaton - Cellular automata in the chemistry lab
• Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia - Cellular automaton

Stanislaw Ulam, while working at the Los Alamos National Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. At the same time, John von Neumann—Ulam's colleague at Los Alamos—was working on the problem of self-replicating systems. Von Neumann's initial design was founded upon the notion of one robot building another robot. This design is known as the kinematic model. As he developed this design, von Neumann came to realize the great difficulty of building a self-replicating robot, and of ...

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Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - History of cellular automata

Patterns of certain seashells, like the ones in Conus and Cymbiola genus, are generated by natural cellular automata. The pigment cells reside in a narrow band along the shell's lip. Each cell secretes pigments according to the activating and inhibiting activity of its neighbours, obeying a natural version of a mathematical rule. The cell band leaves the colored pattern on the shell as it slowly grows. For instance, the widespread species Conus text ...

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Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - Cellular automata in nature

There are many possible generalizations of the CA concept. One way is by using something other than a rectangular (cubic, etc.) grid. For example, if a plane is tiled with equilateral triangles, those triangles could be used as cells. Also, rules can be probabilistic rather than deterministic. A probabilistic rule gives, for each pattern at time t, the probabilities that the central cell will transition to each possible state at time t+1. Sometimes a simpler rule is used; for example: "The rule is the Game of Life, but on each time step there is a 0.001% probability ...

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Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - Related automata

Rule 30 was originally suggested as a possible stream cipher for use in cryptography. Cellular automata have been proposed for public key cryptography. The one way function is the evolution of a finite CA whose inverse is hard to find. Given the rule, anyone can easily calculate future states, but it is very difficult to calculate previous states. However, the designer of the rule can create it in such a way as to be able to easily invert it. Therefore, it is a trapdoor function, and can be used as a public-key cryptos ...

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Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - Uses in cryptography

The simplest nontrivial CA would be one-dimensional, with two possible states per cell, and a cell's neighbors defined to be the adjacent cells on either side of it. A cell and its two neighbors form a neighborhood of 3 cells, so there are 23=8 possible patterns for a neighborhood. There are then 28=256 possible rules. These 256 CAs are generally referred to using a standard naming convention invented by Wolfram. The name of a CA is the decimal number which, in binary, gives the rule table, with the eight possible neigh ...

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Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - The simplest cellular automata

A CA is said to be reversible if for every current configuration of the CA there is exactly one past configuration (preimage). If one thinks of a cellular automaton as a function mapping configurations to configurations, reversibility implies that this function is bijective. For one dimensional CA there are known algorithms for finding preimages, and any 1D rule can be proved either reversible or irreversible. For CA of two or more dimensions it has been proved that the reversibility is undecidable for arbitrary rules. The p ...

See also:

Cellular automaton, Cellular automaton - History of cellular automata, Cellular automaton - The simplest cellular automata, Cellular automaton - Reversible cellular automata, Cellular automaton - Totalistic cellular automata, Cellular automaton - Uses in cryptography, Cellular automaton - Related automata, Cellular automaton - Cellular automata in nature, Cellular automaton - Cellular automata in the chemistry lab, Cellular automaton - Articles on specific cellular automata

Read more here: » Cellular automaton: Encyclopedia II - Cellular automaton - Reversible cellular automata