Chapter 3 of A New Kind of Science reveals that simple rules across many models of computation fall into the same four behavioral classes. This gallery lets you switch among those classes and immediately compare how a cellular automaton, a head-based system, and a tag system express the very same theme.
Each canvas shows 120–200 steps of evolution. Rows correspond to successive steps, read from top to bottom. The cellular automaton colours mark active cells; the Turing machine visualisation tracks tape colours as the head sweeps; the tag system paints the evolving string after each deletion-and-append cycle. Switching classes makes it immediately obvious that—despite their very different mechanics—their long-term behaviour falls into the same categories Wolfram catalogues throughout Chapter 3.