Playground
Type any rule in Wolfram's notation, pick a starting state, and see what universe it makes. Variables that only appear on the right-hand side become brand new elements. Updates use the same standard order as Wolfram's own pictures, so the numbers should match his.
Interactive playground: a rule editor, a starting state, presets from the article, and a big drawing of the network
with controls to run it a generation at a time, view it in 3D, estimate its dimension, show its causal graph and
share a link.
Rules look like {{x,y},{x,z}} -> {{x,z},{x,w},{y,w},{z,w}}. Several rules can be separated by
semicolons. Starting states look like {{1,1},{1,1}}. To keep your browser happy I stop growing at
about 8,000 elements.