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].
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.
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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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.
Webmaster: Mirek Wojtowicz  http://www.mirekw.com |
MCell mirrors: |
Last update: 20 Sep 2001
