BSFKL

BSFKL rules are a multistate generalization of Life-like cellular automata in which live cells that do not survive do not die outright, but instead transition to a third state called "destructive". BSFKL rules are related to but distinct from Generations rules; destructive cells do not decay on their own, as dying cells do in Generations rules, and can kill (and be killed by) live cells.

BSFKL rules were described by Brian Prentice in June 2014, building on an earlier description of a related family of rules described by c0b0p0 in May 2014.

Description

BSFKL rules are described by rulestrings of the form Bb/Ss/Ff/Kk/Ll, an extension of B/S rulestrings, where each of b, s, f, k and l is a group of (unique) numbers between 0 and 8. We write n ∈ B, n ∈ S, ... if n is one of the numbers in b, s, ...; patterns then evolve according to the following rules:

1. A live cell:
   1. dies if it has n destructive neighbors, and n ∈ K;
   2. survives (remains live) if it otherwise has n live neighbors, and n ∈ S
   3. becomes a destructive cell otherwise.
2. A destructive cell:
   1. dies if it has n live neighbors, and n ∈ L;
   2. remains destructive otherwise.
3. A dead cell:
   1. is born if it has n destructive neighbors and m live neighbors, and n ∈ F and m ∈ B.

BSFK rules

BSFK rules are an earlier class of cellular automata described by c0b0p0. These rules are described by rulestrings of the form Bb/Ss/Ff/Kk; unlike with BSFKL rules, f and k are single numbers, and patterns evolve according to following rules:

1. A live cell:
   1. dies if it has k or more destructive neighbors;
   2. survives (remains live) if it otherwise has n live neighbors, and n ∈ S
   3. becomes a destructive cell otherwise.
2. A destructive cell:
   1. dies if it has at least one live neighbor;
   2. remains destructive otherwise.
3. A dead cell:
   1. gets born if it has fewer than f destructive neighbors and n live neighbors, and n ∈ B.

BSFK rules are a strict subset of BSFKL rules; BSFK rule Bb/Ss/Ff/Kk is equivalent to the BSFKL rule Bb/Ss/F0..(f-1)/Kk..8/L12345678.

Extensions

Like Generations rules, BSFKL rules can be adapted to von Neumann and hexagonal neighbourhoods and extended to non-totalistic and non-isotropic rules in a straightforward manner.

BSFKL rules are a subset of the 3-state outer-totalistic rulespace.

Software support

BSFKL rules are not natively supported by either Golly or LifeViewer, but can be run using the Golly's RuleLoader algorithm and a suitable rule table. Catagolue and apgsearch began supporting BSFKL rules on October 29, 2018.

LifeViewer support of BSFKL is planned.

See also

• Generations
• Deficient rule
• List of BSFKL rules investigated on Catagolue

External links

• BSFK rulespace (discussion thread) at the ConwayLife.com forums
• Collection of BSFKL rules on Brian Prentice's website
• Description of the "Java Square Cell" program on Brian Prentice's website