Hex Automata: "Into the Deep" (w/ music). Rule 58 + Seed 30.501

New candidate for the 4-state rule-set library. Cell pattern growth is gradual enough to allow a long run, about twice as long as usual.
The "Celebrity-Splice" rule-set generation method used here splices together individual digits copied from the approximately 40 already existing 4-state rule-sets. Each digit in a new rule-set is copied from the corresponding position of a rule-set randomly chosen from the library (e.g., the 7th digit of a new rule-set comes from the 7th digit of a library rule-set).
Color-coding of cells:
Black (0) -- the dead or empty state,
Red, Yellow, or Blue (1, 2, or 3) -- three different "alive" states.
2-Dimensional cellular automata, hexagonal array,
These 3 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.
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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 Array: size begins at 24 x 24 (columns x rows), grows incrementally, reaching 160 x 160 on time-step 675, and then remains constant.
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 58 full designation:
200000220021231000310010110210100000310200100010001023000030020001030021223332000000231,
This rule-set was generated by using the "Celebrity Splice" method, which joins together individual digits copied from the approximately 50 already existing 4-state rule-sets.
Time: 681 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 30, and reaches a maximum of 2382 on time-step 658, and ends with 1578 on the final time-step 681.
Program: "Hexagon-Multiverse 1.0" (unpublished), PHP language.
Platform: MacBook Pro (M1), Sonoma 14.1.1 OS, Safari 17.1 browser.

[@6AxisSage]

Great description, cheers for sharing ❤ Thats why im at hexagons, cortical column packing in nature!

[@hexagon-multiverse]

The book "Alien Information Theory" by Andrew R. Gallimore (brain & DMT researcher) mentions something relevant, speaking about the human brain: "The smallest functionally-segregated area of the cortex is known as a CORTICAL COLUMN, a cylindrical structure contains about 100 neurons, and the cortex can be described as a mosaic of columns packed side-by-side. At any point in time, the entire cortex displays a complex pattern of activation of these columns." Gallimore gives a reference to the medical literature with more detail. I haven't read that reference, and I don't know about physiology, but I would not be surprised if the cortical columns are arranged in a hexagonal array. I would like to know more about your views regarding these cortical columns.

[@6AxisSage]

@@hexagon-multiverse Sounds pretty interesting, ill look him up. Regarding natural packing of cortical columns, I'll be breaking down my research into a full video with parts and several visualizations including packing, but if you are curious to learn more before that, I recommend Jeff Hawkins thousands brain theory to understand the 6 layers of the neocortex, the hexagons are the bestagons video, videos on neuronal cascade avalanches, evolution of maths from the perspective of naturally occuring yet geographically seperated cultures starting with a natural affinity for base 6 counting systems.