0 fps
This is an elementary cellular automaton: each cell's next state depends only on itself and its two immediate neighbours, giving 8 possible neighbourhood patterns whose 8 output bits define a rule number from 0 to 255. Rule 30 famously produces chaotic, seemingly random output from a single starting cell, while Rule 90 builds a Sierpiński triangle and Rule 110 is Turing-complete.
Generation after generation of a 1D cellular automaton stacked vertically, where each row's pattern is generated purely from the row above it using the selected rule's 8-bit lookup table.
Pick a Rule preset (30, 90, 110, 184, 250) or set a custom Rule number, choose Single or Random initial condition, adjust Cell size and Speed, then use Reset, Pause, Step, Random rule or Save PNG.
Rule 30's centre column has been used as a random number generator in Wolfram Mathematica — a strikingly simple 3-neighbour rule producing output that passes many statistical randomness tests, despite being fully deterministic.
Each cell has 3 relevant neighbours (left, self, right), giving 2³=8 possible input patterns. The rule number's binary representation supplies exactly 8 bits, one output (0 or 1) per pattern — that's the whole automaton's behaviour packed into one byte.
Rule 90 is a simple XOR of the two side neighbours (ignoring the centre entirely), which recursively builds the self-similar Sierpiński triangle; Rule 30's lookup table has no such symmetry, so tiny local interactions cascade into globally unpredictable, statistically random-looking patterns.
Rule 110 has been mathematically proven Turing-complete — meaning, with the right initial configuration, it can in principle simulate any computer program, making it one of the simplest known systems capable of universal computation.
Starting from a Single black cell shows how complexity can emerge from one point of "disturbance" in an otherwise empty row; starting from Random noise instead reveals how a rule filters, amplifies or organizes existing disorder rather than creating it from nothing.
It records just the middle cell's value across the last 48 generations as a bit sequence — this is the exact metric that showed Rule 30's centre column behaves statistically like a coin flip, which is why it was proposed as a pseudorandom number source.