Ian Stewart has written many books, so he has nothing to prove in terms of being a successful author who explains difficult topics in an accessible way. This book seems to be very close to another of his, first published in 2001, called “What Shape Has a Snowflake?” (Ivy Press). The present version, also with this publisher, but also MIT Press, has improved new pictures as well as a better title, but the text is more or less unchanged. The text does not need to change, though some on page 162 shows its age. Professor Ian Stewart is the David Attenborough of the genre and his style is fluent, readable, informative and confident.

This is a splendid book. The excellent prose is enhanced by spectacular pictures. It is breath-taking in its scope, and the layout is refreshing. Each topic is confined largely to just two sides, the open page. The book is so well written with no wasted words that this works. There are three parts: Principles and Patterns, The Mathematical World, and Simplicity and Complexity––sixteen chapters in all. The first three start with snowflake hexagonal symmetry, honeycombs, then other two-dimensional curves from nature, finally introducing three dimensional patterns. This leads to the largest middle part of the book with over 100 pages (eight chapters) that go into more technical detail. He somehow does this without the need to understand any actual mathematical symbolism. It is a tribute to Stewart’s explanatory powers that he manages to do this with success. Here the section on animal stripes stands out as does that on animal gait; these are research topics for Stewart, but once more there’s no mathematics here, just clear exposition. There is much more, from astronomy, architecture, patterns in time, even packing fruit in a box. The final section, five chapters, goes into complexity, fractals and chaos. The book is philosophical, beautifully written, artistic and with a touch of humour (Stewart has co-authored with the late Terry Pratchett, and written science fantasy). Stewart has authored a lot of books, all worth reading. This just might be the best of them.