A new rule-set, notable for its ability to maintain dynamic complexity for a long time without growing too large.
This new rule-set was found by the "Average-Biased Random" method, which compares 68 published rule-sets to each other, one binary digit (0/1) at a time. The average is taken for the 1st binary digit across all rule-sets. Then the average is taken for the 2nd digit, and the 3rd, etc, for all digits. These averages (between 0 and 1) are then used as probabilities to bias a pseudo-random number generator to give new rule-sets with binary digit values (0 or 1) similar to the average.
For example, if the average for the 4th binary digit was 0.63, then the probability of a "1" appearing as the 4th digit in a new rule-set is 63%. This method gives a higher success rate than the other search methods tested so far, but it cannot sample the entire vast rule-space (as a pure random search can).
Digits can occasionally (with lower relative probabilities) be assigned the opposite of the favored value, thereby allowing some novelty not already possessed by the original 68 rule-sets.
Video title inspired by Locutus of Borg:
• TNG I am Locutus of Bo...
2-Dimensional cellular automata, hexagonal array,
Color-coding of cells age/life-status:
All colored cells are alive except blue-colored cells.
yellow = just born (state = 1),
red = alive 2 or more time-steps (state = 1),
blue = fading "ghost" of cell that died (state = 0),
black = empty space (state = 0),
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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: begins at 36 x 36 (columns x rows) and grows incrementally to 140 x 140 on time-step 293, and then remains constant all the way to the final time-step 942.
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).
Neighborhood: semi-totalistic (details to be published at a future date),
Rule-set 392 full designation: 81180 - 912 - 3472 - 245034,
Found by using the "Average-Biased Random" search method for generating new rule-set candidates.
Time: 942 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 72, and reaches a maximum of 1518 on time-step 318, and ends with 822 on the final time-step 942.
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.