This run is the first to simultaneously use the "auto-zoom" and "history shading" program functions. This is to verify that these functions are now compatible on the square-shaped hexagonal grid. Auto-zoom code had to be completely reorganized, but is now much simpler & efficient.
"Auto-zoom" automatically enlarges the cell grid to keep a growing fractal object fully within the viewing screen. But it has the option to stop the grid expansion at a pre-chosen time, as occurs in this run (see details below).
"History shading" uses shades of gray to display which cells have been previously alive. Here the "fast fade" setting is used, which causes the gray shading to fade to black at a user-specified rate. This creates a nice "vapor trail" effect for spaceships.
Next, this same test will be repeated, but with the hexagon-shaped hexagonal grid instead of the square-shaped hexagonal grid.
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),
gray = cells that have been previously alive
(more recently alive cells are shown as brighter shades),
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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 starts at 28 x 28 (columns x rows), and expands to maintain the growing seed in-frame, reaching 76 x 76 on time-step 94 (after about 19 seconds). The grid has increased in size 6 times by this point. After this, the grid size remains constant, allowing the spaceships to wrap across the screen edges.
Periodic boundary conditions: horizontal & vertical dimensions wrap across opposite edges, giving a topology equivalent to the 2-dimensional surface of a 3-dimensional torus (doughnut/donut).
Neighborhood: semi-totalistic (details to be published at a future date),
Rule-set 342 full designation: 71680 - 516 - 2322 - 114044,
This rule-set was generated by the "celebrity splicing" method: combining "genetic material" (strings of 0s & 1s) taken from 4 different rule-sets randomly chosen from the 63 currently published rule-sets.
Time: 298 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 21, and first reaches a maximum of 554 on time-step 253, and ends with 554 again on the final time-step 298.
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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