256 Little Worlds
A row of cells, each on or off. Each new row is made from the one above by a rule that looks at a cell and its two neighbours: eight cases, so 28 = 256 possible rules. Pick one and watch what it builds.
Top of each block: the three cells (left, self, right) in the row above. Bottom: the cell in the new row. Click a block to flip its outcome; the rule number is the eight outcomes read as a binary number.
What to look at
Rule 90 draws the Sierpiński triangle: each cell is the XOR of its two neighbours, so it is Pascal's triangle taken mod 2. Rule 30 looks random from one single cell; Wolfram used its centre column as a random number source. Rule 110 is known to be able to compute anything a computer can (Cook, published 2004). Rule 184 moves "cars" right without ever losing one, a model of traffic. Rule 0 and rule 255 do nothing interesting, and there are a lot of rules like them.
Checked by the page
The edges wrap around (the row is a ring), except for the checks on one cell where the row is wide enough that the pattern never reaches the edge. Wolfram's numbering and the history are from memory; the checks above are computed.