Agar

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An agar is any pattern covering the whole plane that is periodic in both space and time. In other words, they are the shift periodic configurations contemplated by symbolic dynamical systems theory, although this characterization is not always followed rigorously. Low entropy and a semblance of order is the real criterion; there are several possibilities:

  • strict periodicity according to a compatible lattice group,
  • degenerate one dimensional periodicity (ripples),
  • symmetry arising from a second stage de Bruijn diagram,
  • color symmetry following a Shubnikov group,
  • irregular with the symmetry of a superlattice,
  • fractal symmetry described by a Lindenmayer system, or
  • they just look pretty.

Any set of bounded patterns may be laid side by side, provided that they are sufficiently separated, and still not be seen as an agar. For example, that is the difference between still lifes and pseudo still lifes. As a restricted class of Life patterns, agars often subject to mathematical or computational analysis. If they were much more arbitrary, they would be called soups or ash.

The following tables show examples of linear and tiling agars. Refer to each link for building methods and more variations than may be shown here.

Line agars

Agar density period stable notes image
Zebra stripes 1/2 - B (1) alternating bands of live and unoccupied cells (ripples(2)) LINEZB.GIF
Venetian blinds 1/2 2 B phoenix made of fat ripples, varying only longitudinally (2) LINEVB.GIF
Chicken wire 1/2 2 B wires have a uniform height of 2 but with gaps at least 2 cells wide LINECW.GIF
Diagonal ripples 7/20 - S diagonal strands which can occur singly, in pairs or mixtures separated by at least two cells. Transient evolution eventually comes to rest periodically, including vanishing LINEDG.GIF
Phoenix - 2 the avatar filaments can be separated, and possibly terminated as barberpoles LINEPH.GIF
  1. S, stable ; B, must be bound on two or four sides ; for common bounds see Dean Hickerson's list[1].
  2. Cross sections following Wolfram's (2,1) Rule 22.
  3. Cross sections following Wolfram's (2,2) Rule 01140238X

Tile agars

Agar tile size box density period stable notes Image showing unit cell and 2x2 cell
Onion rings 72 12*12 1/2 B unit cell composed of nested squares (4n x 4n) ; static on a color lattice (complementary sublattices alternate checkerboardwise) TILEOR.GIF
Marshland agar 4 3*3 4/9 S built from ponds and lakes, that is, dominoes ; of many possible combinations, only basic ones go squared TILEML.GIF
Houndstooth agar 8 4*4 1/2 2 B really the pattern of a known checquered twill TILEHO.GIF
Herparian agar 12 6*6 1/3 S lakes made of snakes acting like dominoes ; only the most basic give a square tiling TILEHA.GIF
Herparian agar 12 6*6 1/3 S snakes polymerize in three ways; the unit cell of this agar is oblong TILEHB.GIF
Squaredance 8 6*6 2/9 2 B period 2 diagonal agar and phoenix, low density domino pattern TILESD.GIF
Scrubber 2 period 2; odd generations = Piston, even generations = Scrubber TILEPS.GIF
Reciprocating agar 2 period 2; Test tube baby can be elongated, rotated, stabilized, to get numerous tiles. Packable regularly or irregularly into the cartesian plane, none is necessarily a unit cell. RCPAAGR.GIF

References

  1. Dean Hickerson's oscillator stamp collection.

See also

External links

  • Agar at Eric Weisstein's Treasure Trove of Life
  • Agar at the Life Lexicon