On 2022-08-01, Rudy Rucker, mathematician, science fiction author, professor of mathematics and computer science, artist, and my occasional co-author, gave a talk at the Bridges Conference on Mathematics and the Arts at Aalto University in Helsinki, Finland. His theme was how art, like much of what is interesting in the mathematics of dynamical systems and physics, occurs on the border between regularity (like the thump-thump-thump of a drum machine) and randomness (white noise). A written version of the talk (actually, quite a bit different) with high-resolution images of the paintings is posted on Rudy’s blog.
The edge between regularity and chaos is illustrated by the behaviour of cellular automata, which Stephen Wolfram has characterised into four classes, with Class 4 balanced on the edge. Some Class 4 automata have been demonstrated as capable of universal computation, and Wolfram speculates that most, if not all are universal. I discuss this as being part of the secret of life in my 2004 paper “Computation, Memory, Nature, and Life”.