Another experiment with the "universal replicator" rule-set implemented on the edge-wrapped hexagonally-shaped grid of hexagonally-spaced cells. Also checking the totalistic color palette.
Can 3 objects be replicated together in the same run? The thumbnail and the beginning of this video show that the 3 seeds can replicate independently on the same screen if separated far enough apart from each other. But what happens after the 3 expanding patterns overlap?
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).
2-Dimensional cellular automata, hexagonal array,
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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: radius remains constant at 60 cells.
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),
Rule-set found by random search. Details to be published later.
Time: 256 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 202, reaches a maximum of 5828 on time-step 127, and finishes with 1152 on the final time-step 256. Note that the final population is slightly less than 6 x 202 = 2904 due to overlap between some of the copies.
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.
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