Testing to ensure that the newly added "history shading" function ("fast-fade" option) works properly with the hexagonally-shaped field of cells. Upcoming videos will test various combinations of program settings that have thus far not been tried together. Must try to root out all conflicts before translating the program into the Kotlin language.
I just noticed that these ships are moving slower than usual -- only 0.5 cells per time-step, which half of the maximum speed of 1 cell per time-step (the "speed of light" in this automaton). This is one of the few ships which have been spotted traveling at sub-light speed. The vast majority of ships seen so far in various rule-sets travel at light speed.
The same rule-set & spaceship also appear in these videos:
"Ships & Oscillators": • Hex Automata: "Ships ... ,
"Warp Tubes": • Hex Automata: "Warp T... ,
Color-coding:
YELLOW cells are just born,
RED cells have been alive 2 or more consecutive time-steps,
BLUE cells are already deceased, but their "ghost" lingers for 1 time-step.
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 56 cells.
Periodic boundary conditions: opposite pairs of edges are screen-wrapped, giving a topology equivalent to the 2-dimensional surface of a 3-dimensional torus containing a 180 degree twist. The twist does have a noticeable effect (compared to a screened-wrapped rectangular field which corresponds to a torus with no twist).
Neighborhood: semi-totalistic (details to be published at a future date),
Rule-set 325 full designation: 21980 - 4896 - 1840 - 78805,
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 all currently published rule-sets.
Time: 370 steps (display rate 5 fps). The first & final frames are shown for 1 & 2 seconds, respectively.
Live cell population: starts at 161 (6 spaceships), and fluctuates between 161 and 170 until time-step 200 (when a ship is destroyed), then fluctuates between 135 and 141, and ends with 139 on the final time-step 370.
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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