Game of Life
A cell lives if it has 2 or 3 live neighbours, and a dead cell with exactly 3 neighbours comes alive (the B3/S23 rule). Click or drag on the grid to draw. The edges wrap around.
Elementary (1D)
Each new row comes from the three cells above it, so 8 patterns map to 8 output bits, which is the rule number. Rule 30 is chaotic enough that it was used as a random-number generator in Mathematica; Rule 90 draws a Sierpinski triangle; Rule 110 is Turing-complete.