The replicator rule-set (which makes copies of any seed) is being tested for robustness of replication fidelity. A single small change to the cell pattern about halfway through the simulation run, in order to see how the final cell pattern is affected.
A single live cell is deleted from the left edge of the central live cell clump at time-step 132. The effects of this change spreads throughout the entire pattern during the next 124 time-steps (for a total of 256 time-steps).
For comparison, the control run (same simulation run but without the change described above) is shown in the video "Hello Replicator".
• Hex Automata: "Hello ... ,
Both videos (control run & altered run) are identical for the first 131 time-steps, but then begin to deviate at time-step 132 (at 27.4 seconds).
Simply from comparing the thumbnails for the 2 videos, we can see that deleting a single cell caused noticeable message degradation and general noise throughout the overall pattern. On the other hand, considering that the message is still legible at all at the end of the run, this rule-set might be above average at maintaining coherence/self-correction in the presence of small amount of noise (added and/or deleted live cells).
In this video, the usual "Age-based" color-coding is used:
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: size remains constant at 140 columns x 140 rows.
Periodic boundary conditions: horizontal & vertical dimensions wrap across opposite edges, giving a topology equivalent to the 2-dimensional surface of a 3-dimensional torus.
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 136, fluctuates wildly, reaches a maximum of 10088 on time-step 123, and ends with 1752 (6 noisy overlapping copies of the original seed) on the final 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.
Негізгі бет Ғылым және технология Hex Automata: "Glitch in the Matrix" Rule 304 + Seed 136.502
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