Cellular Automata rules lexicon

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Family: Weighted Generations

Type: totalistic or outer totalistic parameterization with optional decay

Weighted Generations family, discovered and explored in 2001 by Brian Prentice, is a natural extension of the Generations family. The extension simply permits any state to contribute to the neighbor count using weights associated with each state. If a weight is n, and the corresponding state occurs m times in a cells neighborhood then the neighbor count is incremented by n*m. If a state's weight is 0, then that state does not contribute to the neighbor count. Position weights identical to those used in the Weighted Life family are also supported.

Weighted Generations family is implemented as a configurable user DLL, supported by MCell starting with version 4.20. The rule setup is controlled by an input dialog window. This window is shown below with the parameters set for Conway's Life.

The weights of neighbors and state weights can be set within a range [0..10].

Rule Notation

The notation of rules in "Weighted Generations" consists of 5 different keywords, specified in any order:
C, SW, PW, RS, and RB.

C - specifies the count of states, 2..16.
SW - specifies the ordered, semicolon-separated list of weights of states 0..C-1.
PW - specifies the semicolon-separated list of position weights, in the following order: NW, N, NE, W, E, SW, S, SE.
RS - specifies the semicolon-separated list of totals allowing cells to survive.
RB - specifies the semicolon-separated list of totals allowing cells to be born.

MCell built-in Weighted Generations rules

The following 11 rules exemplify Brian's pattern collection. Each of the selected rules demonstrates the unusual behavior of the Weighted Generations' family. They are divided into 4 types:
General Purpose - pattern generators dream rules: rules 004, 050, 071 and 072
Puffers and Ships - great for constructing complex ships: rules 031 and 063
Diagonal Puffers and Ships - support the construction of complex diagonal ships: rules 012 and 020
Irregular - examples of the unusual nature of the rule family: rules 038, 074 and 84

Name Character Rule Description
WG Rule004 Chaotic
This rule is a close relative to the famous Star Wars rule and like that rule is a pattern developers dream. All basic types of patterns are supported. The rules potential for generating interesting patterns can be demonstrated by observing the development of any one of the five chaos patterns (C001.mcl through C005.mcl).
A rule by Brian Prentice, May 2001.
WG Rule050 Chaotic
This rule supports a broad range of patterns including ships, puffers, diagonal ships, diagonal puffers, and still life. Ships with speeds of c/2, c/3 and c/5 have been found.
A rule by Brian Prentice, June 2001.
WG Rule071 Chaotic
A delightful rule supporting unusual guns, oscillators, ships and puffers. The rule does not however, seem to support diagonally moving objects.
A rule by Brian Prentice, June 2001.
WG Rule072 Chaotic
This rule supports a rich assortment of guns and oscillators together with ships, puffers and still life. No diagonally moving patterns have yet been found.
A rule by Brian Prentice, June 2001.
WG Rule031 Chaotic
At first this rule seems not to have much potential but from its simple building blocks really complex puffers and ships can easily be built.
A rule by Brian Prentice, June 2001.
WG Rule063 Chaotic
Generates many unusual puffers and ships. Ships with speeds c/2, c/3, 9c/31 and c/5 have been found (see SD002)
A rule by Brian Prentice, June 2001.
WG Rule012 Chaotic
This rule seems only to support diagonally moving ships and puffers and still life. No regular ships, puffers or oscillators have yet been found. The diagonally moving puffers are very unusual and quite rare. Four such puffers have been found so far, some of which are quite complex (see DP002.mcl). Diagonal moving ships (gliders) with three different speeds have been found including some that travel faster than Life's glider (see SD001.mcl).
A rule by Brian Prentice, June 2001.
WG Rule020 Chaotic
This rule is unusual in that from a random soup it quickly transforms into many small diagonally moving ships. It also supports diagonal puffers.
A rule by Brian Prentice, June 2001.
WG Rule038 Chaotic
An Irregular rule which is a good example of the unusual nature of the rule family. The guns are particularly interesting.
A rule by Brian Prentice, June 2001.
WG Rule074 Chaotic
This rule is notable for its diagonal puffers which lay closely packed tiles consisting of oscillators and for the unusual nature of its oscillators and stretchers.
A rule by Brian Prentice, July 2001.
WG Rule084 Chaotic
This rule supports diagonal puffers and diagonal ships. It also generates a set of ships resembling Pascal triangles which can be constructed of any size (see S010).
A rule by Brian Prentice, July 2001.

To see a collection of patterns generated by Weighted Generation rules download Brian's WG library. The library is updated regularly and currently contains more than 2000 patterns from over 100 rules. A smaller collection consisting of some of Brian's more interesting patterns together with all the 'Knight Ships' is included with the MCell distribution.


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Last update: 20 Sep 2001