Скачать или смотреть Pure Symmetry ♫

For a seed's symmetry to be conserved over the long term, the space in which it grows must have the same symmetry as the seed. In this instance, the 4-fold rotational symmetry of the seed is conserved throughout the run by using a square field of cells (equal numbers of columns and rows). Note that squares have 4-fold rotational symmetry.

If instead a rectangular field of cell is used (with unequal numbers of columns and rows) , the 4-fold symmetry of the seed will tend to reduce a pattern with only 2-fold symmetry. This happens because self-collision via screen-wrapping won't be simultaneous for the horizontal and vertical dimensions.

2-Dimensional cellular automata, square cell grid,

Semi-totalistic ruleset Leela-9 + Seed 12.501.

This automaton uses "totalistic" color-coding of live cells:
Black -- empty/dead cell,
Violet (Lavender Magenta) -- live cell with 0 live neighbors,
Sapphire Blue -- live cell with 1 live neighbor,
Emerald Green -- live cell with 2 live neighbors,
Gold -- live cell with 3 live neighbors,
Copper -- live cell with 4 live neighbors,
Ruby Red -- live cell with 5 live neighbors,
Silver -- live cell with 6 live neighbors.
Indigo -- live cell with 7 live neighbors,
Teal -- live cell with 8 live neighbors.

Square cell grid: size remains constant at 60 columns x 60 rows.

Periodic boundary conditions: horizontal & vertical dimensions wrap across opposite edges, giving a finite closed continuous surface equivalent to a 2-torus (the surface of a standard 3-d ring donut).

Time: 297 steps (at 5 frames per second).

Program: "CA Explorer" (unpublished), PHP language (8.1.8).
Platform: MacBook Pro (M1) processor, macOS Sequoia 15.5, Safari 18.5 browser.