Hex Automata: "What the Hex?". Rule h1 + Seed h25.501

The rule-sets in this new 6-state cellular automata (CA) produce cell patterns that are generally more strange than those from the 2-state CA. The 2-state CA rule-sets are based on a simple property of the live cell pattern -- the total number of live neighbors. By contrast, the 6-state CA uses rule-sets that are not based on any such organizing principle -- they are totally abstract. And these rules produce patterns unlike any I have seen before.

All previous CA here have had 2 states -- every cell is either dead (0) or alive (1). To more fully explore automata-space, Hexagon-Multiverse will have an option for cells to have 6 states (0 = dead, 1-5 = alive), with each of these six states indicated by a different cell color.

The number of different possible rules ( the size of the "rule-space") for this new 6-state CA is a mind-numbing 6*63 (6 raised to the 63rd power) which is 1.0556714 x 10*49 (ten trillion trillion trillion trillion). This rule-set used in this video was found after only 30 random tries, so this rule-space might be rich with interesting forms.

2-Dimensional cellular automata, hexagonal array,

Color-coding for cells with 6 states:
5 alive states: violet, blue, yellow, red, & silver,
1 dead state: black,

These 5 different alive states do not correspond to any simple property of the cell pattern. This is unlike commonly seen totalistic ("sum-of-neighbors") rule-sets. Here each of the 6 states is assigned to a randomly chosen subset of the 63 possible neighborhood configurations.

So far the rule-set searches with this new CA are purely random, except that the "0" state is biased to have a 50% chance of appearing at each of the 63 rule-set digits. The rule-set is written as a 63-digit base-6 number (only digits 0-5 ). For this run, the nickname "rule h22" refers to the full rule-set:

052503005104031002100030310302500000010000000011020320000000300,

---------------------------------------
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.
---------------------------------------
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 Array: size remains constant at 120 columns x 120 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).

Rule-set h1 full designation:
445000000400250050001100002202403002340300000035335010500200020,
This rule-set was found by random search.

Time: 396 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.

Live cell population: starts at 25, and reaches a maximum of 5176 on time-step 246, and then ends with 4016 on the final time-step 305.

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.