Agar
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 in symbolic dyamical systems theory, although this characterization is not always followed rigorously. Low entropy and a semblance of order is the real criterion; for instance the chicken wire pattern follows strict transversal periodicity 2, but almost any longitudinal mesh length is acceptable.
Agars show little computable action. They offer research subjects for tiling, combinatory operations, bounding needs and methods.
Must an agar be stable or of period 2 ? There might be some of period 3, or more, depending the way one defines them, strictly or not. A plain set of still life patterns may be laid side by side and still not be seen as an agar.
One criterion is stability ad infinitum.
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 |
|---|---|---|---|---|
| Zebra stripes | 1/2 | - | B (1) | alternating bands of live and unoccupied cells (ripples(2)) |
| Venetian blinds | 1/2 | 2 | B | phoenix made of fat ripples, varying only longitudinally (2) |
| Chicken wire | 1/2 | 2 | B | wires can have any length, at least 2, and need not all be the same |
| Diagonal ripples | 7/20 | - | S | ripples, stable (and progenitor of tubs and barges) when double ; most vanish instantly |
- S, stable ; B, must be bound on two or four sides ; for common bounds see Dean Hickerson's list[1].
- Cross sections following Wolfram's Rule 22.
Tiling agars
| Agar | tile size | box | density | period | stable | notes |
|---|---|---|---|---|---|---|
| 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) | |
| Marshland agar | 4 | 3*3 | 4/9 | S | build of ponds and lakes, that is, dominos ; many possible combinations, only basic ones go squared | |
| Houndstooth agar | 8 | 4*4 | 1/2 | 2 | B | really the pattern of a known checquered twill |
| Herparian agar | 12 | 6*6 | 1/3 | S | lakes made of snakes acting like dominos ; only the most basic give a square tiling | |
| Squaredance | 8 | 6*6 | 2/9 | 2 | B | period 2 diagonal agar and phoenix, low density dominos pattern |
References
See also
External links
- Agar at the Life Lexicon