Saturday, September 04, 2021

[kqmhkgbb] end states of Life

a categorization of how patterns (e.g., methuselah) can settle down in Conway's Game of Life:

  1. zero cells alive (diehard)
  2. limited bounding box, still life
  3. limited bounding box, oscillator
  4. no bounding box, limited population, only glider(s) escape
  5. no bounding box, limited population, some other spaceship escapes
  6. no bounding box, limited population, something other than a spaceship goes outward, e.g., two objects whose separation distance which slowly increases due to reactions with a glider shuttling between them.  i think a simple example exists of a fleet of gliders pushing a block outward, reflecting one glider back.  the returning glider triggers production of the next outward fleet of gliders.
  7. no bounding box, infinite growth: many subcategories

there is overlap among the categories, e.g., a pattern could result in an escaping glider, interesting spaceship, and infinite growth.  the non-escaping portions of the limited population of 4 and 5 could be classified 1, 2, or 3.

additional category: chaotic behavior, no one knows how it will turn out.  this is frequently seen in other cellular automata rules, and, because Conway Life is universal, it is possible in it as well.  (useful building block: 0E0P metacell.)  Real Life is probably in this category, though heat death of the universe could be interpreted as category 1.

category 1 feels nihilistic: we all die in the end.

categories 4 and 5 can be made to fit in a box (converting to 1, 2, or 3) by pre-placing distant objects to destroy escaping spaceships.  cleanly destroying (to achieve category 1) a dense flotilla of gliders might be tricky, as might be cleanly destroying an escaping spaceship of category 5.

infinite growth can be subcategorized by growth rate: sublinear, linear, superlinear but subquadratic, quadratic.  categorize sawtooth growth by its envelope over time.

linear growth subcategories: gun, puffer train, wickstretcher, other.  (i don't know of anything in "other".  maybe a hypothetical pattern that grows as a spiral.)  the boundary between puffer train and wickstretcher is hazy.

puffer train subcategories: rake, non-rake.  there is overlap: puffer exhaust can be a combination of escaping spaceships and non-spaceship debris.  rakes can be subdivided by the type of emitted spaceship and the direction the emitted spaceships travel relative to the puffer.  again, overlap possible if multiple types of spaceship in the exhaust.

quadratic growth subcategories: breeder, spacefiller, other.  metacatacryst is on the boundary between breeder and other.

chaotic growth could be on the boundary between spacefiller and other.  chaotic growth can also have any growth rate, often unknown, not necessarily quadratic.

breeder subcategories: {M,S}^3.

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