Trying out a different color palette for totalistic color-coding of cells. The rule-set used here is the "Universal Replicator", which makes copies of any seed.
The seed, grid shape, and cell neighborhood all have perfect hexagonal (6-fold rotational) symmetry, which is preserved through the entire run.
The overall cell pattern sometimes shows a slight twist around the center of the grid -- caused by the "twisted-torus" topology of the screen-wrapped hexagonally shaped cell grid.
Video title inspired by hipster Cosmo Kramer:
• Kramer And The Amazing... ,
2-Dimensional cellular automata, hexagonal array,
Totalistic Color-coding for cells with 0 to 6 live neighbors:
violet = 0 live neighbors,
blue = 1 live neighbor,
green = 2 live neighbors,
yellow = 3 live neighbors,
orange = 4 live neighbors,
red = 5 live neighbors,
white = 6 live neighbors,
black = dead cell/empty space.
(This color palette is still being optimized).
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General Procedure:
STEP 1). Make a 2-dimensional grid (array) of "cells" which can each have a value of 0 (off/dead) or 1 (on/alive). Conway's famous "Game of Life" cellular automaton uses a square grid, but here we use a hexagonal grid (chicken-wire or honeycomb). Initialize the grid by filling it with all zeros. This is the "main grid".
STEP 2). Add a starting "seed" pattern to the main grid by changing some of the cell values to "1" (on/alive). Sometimes specific compact seeds are used, alternatively sometimes they are a random unstructured spread of ones that II call "primordial soup".
STEP 3). The program then looks at every cell in the entire main grid, one-by-one. When examining each cell, the total number of live neighbor cells is counted among its 6 immediately adjacent neighbor cells (if using "totalistic" rules). The program then consults the rule-set to decide if the central cell will be alive (1, on) or dead (0, off) in the next time-step. In order to not disturb the cell pattern that is being updating, all of these new values are accumulated on a separate "temporary grid".
STEP 4). After every cell is updated on the temporary grid, the main grid is re-initialized to all zeros, and then the temporary grid is copied to the main grid
STEP 5). Repeat Steps 3 & 4 for hundreds or thousands of iterations. The result of each iteration serves as the input for the next iteration. The grid is finite, so the live cell pattern will eventually go repeat or go extinct, although this could take thousands of time-steps.
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Note: this "Hexagon-Multiverse" (HMCA) cellular automaton is similar to Conway's famous "Game of Life" in the sense that both are 2-dimensional, have binary cell states, and are synchronous and deterministic. But the Game of Life uses a square grid, while the HMCA uses a more natural (common in nature) and more symmetrical hexagonal grid. Additionally, the HMCA achieves interesting results using a variety of rule-sets, whereas the Game of Life is limited to a single rule-set.
Hexagonal Cell Grid: size remains constant at a radius of 40 cells (extending from the center cell to each of the 6 directions).
Periodic boundary conditions: a hexagon-shaped grid has 3 pairs of opposite edges wrap to give a finite closed continuous surface equivalent to a 2-torus (the surface of a standard 3-d ring donut), but containing a 180 degree twist.
Neighborhood: semi-totalistic (details to be published at a future date),
Time: 256 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 19, and reaches a maximum of 3162 on time-step 127, and ends with 114 on the final time-step 256.
Resolution: 2578 screen pixels per cell,
Program: "Hexagon-Multiverse 1.0" (unpublished), PHP language.
Platform: MacBook Pro (M1), Sonoma 14.1.1 OS, Safari 17.1 browser.