The Science of Patterns Mathematics is the science of patterns. A pattern is a landmark in the magical maze. Many common types of pattern are symmetric. Symmetries are widespread. We find them in kaleidoscopes, allowing us to design bathroom mirrors that don't reverse left and right.
Slime mould is a crowd of amoebas, which assemble in beautiful spiral patterns.
These patterns 'emerge' from mathematical rules that govern chemical signals sent from each amoeba to its neighbours. The same kind of rotating spiral can be observed in a beautiful chemistry experiment, the Belousov-Zhabotinskii reaction. The mathematics of such patterns, introduced by Alan Turing, also applies to the markings on animals. Others, such as leopards or giraffes, have spots. Turing suggested that chemical patterns in embryos could lay down a 'pre-pattern' which, when the animal developed, triggered the formation of the markings that we see.