Clearer Hexplication

Описание: This run uses the same rule, seed, and other settings as in the previous run, except that totalistic color-coding is used this time. The totalistic color scheme simply assigns a specific color to each possible total number of live neighbors (0, 1, 2, 3, 4, 5, 6). Only the immediately adjacent (touching) neighbors count.

The alternative "age-based' color-coding scheme shows live cells as well as recently "deceased" cells (blue "ghosts" lingers for 1 time-step). Such inclusion of "ghosts" is a useful and desirable option, but it can obscure details of the live cell pattern. By contrast, totalistic color shows only live cells, giving a clearer view.

The "universal replicator" rule 304 is used, in order to figure out the details of how the rule is implemented. (I already know the rule, but want to see if we can tease it out based on visual inspection alone). The full details will be released soon. So far we know that live cells with zero live neighbors die, and that dead cells with one live neighbor become alive. Here is a new clue: rule 304 is completely totalistic.

Here the rule is implemented on the edge-wrapped hexagonally-shaped grid of hexagonally-spaced cells. Since the topology of the closed 2-d edge-wrapped surface is a 2-torus with a 180 degree twist, cells patterns with an added twist are often seen, regardless of the rule-set used.

2-Dimensional cellular automata, hexagonal array,
Rule 304 + Seed 1.001.

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.

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 begins at 32, then grows in increments , reaching radius 60 on time-step 52, and then remains constant.

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 1, reaches a maximum of 6072 on time-step 63, and finishes with 6 (6 copies of the seed) on time-step 256.

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.