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Rule 30 has also been used as a random number generator in Mathematica, [3] and has also been proposed as a possible stream cipher for use in cryptography. [4] [5] Rule 30 is so named because 30 is the smallest Wolfram code which describes its rule set (as described below). The mirror image, complement, and mirror complement of Rule 30 have ...
Rules which are the same as their mirrored rule are called amphichiral. Of the 256 elementary cellular automata, 64 are amphichiral. The second such transformation is to exchange the roles of 0 and 1 in the definition. The result of applying this transformation to a given rule is called the complementary rule. For example, if this ...
Default generator in R and the Python language starting from version 2.3. Xorshift: 2003 G. Marsaglia [26] It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence.
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 that each cell will transition to the opposite color."
L-system trees form realistic models of natural patterns. An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a ...
The first rule reads: A S consists of a NP (noun phrase) followed by a VP (verb phrase). The second rule reads: A noun phrase consists of an optional Det followed by a N (noun). The third rule means that a N (noun) can be preceded by an optional AP (adjective phrase) and followed by an optional PP (prepositional phrase). The round brackets ...
Zipf's law (/ z ɪ f /; German pronunciation:) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language:
The various FBI mnemonics (for electric motors) show the direction of the force on a conductor carrying a current in a magnetic field as predicted by Fleming's left hand rule for motors [1] and Faraday's law of induction. Other mnemonics exist that use a right hand rule for predicting resulting motion from a preexisting current and field.