Which rules turn a single live cell into a regular, a nested or an irregular pattern? Rule 30 grows a triangle from the center cell that is regular along its left edge and irregular everywhere else.
Try this Set error-probability to 0 and rule to 90, then press Reset. The single cell grows a nested Sierpinski triangle. Rule 110 grows only to the left, with irregular structures inside.
About this model Where it ends up
The elementary cellular automata Stephen Wolfram catalogued in 1983. A row of cells updates each cell from itself and its two neighbors by one of 256 rules. This version draws each generation as the next row down, so the board is the full history, and can inject flip errors to mark which later cells could depend on them.
Setup lights the center cell of the top row or, with seed-mode set to random-density, each top cell at cell-density percent. Each tick writes the next row. Every cell reads the three cells above it (the row wraps left to right) and looks up its value in the 8 bits of rule. The run stops after 128 generations, when the bottom row is written. rule is read every tick, so changing it mid-run switches rules from the next row down; seed-mode and cell-density apply at Reset.
At error-probability percent per row, one random cell of the new row is flipped and shown red. Every cell below with a marked cell among its three parents is marked too and painted the flip's color, live or dead alike. The marked region is the flip's light cone and widens by exactly one cell per side per row whatever the rule, so it shows which cells could depend on the flip, not which ones changed, and it hides the pattern inside it. NetLogo's CA 1D Elementary has no flip errors; they are an addition here.
