Algorithmic Beauty of Sea Shells

The pigment patterns on tropieal shells are of great beauty and diversity. They fas- cinate by their mixture of regularity and irregularity. A partieular pattern seems to follow partieular mIes but these mIes allow variations. No two shells are identical. The motionless patterns appear to be static, and, indeed, they consist of calcified material. However, as will be shown in this book, the underlying mechanism that gene rates this beauty is eminently dynamic. It has much in common with other dynamie systems that generate patterns, such as a wind-sand system that forms large dunes, or rain and erosion that form complex ramified river systems. On other shells the underlying mechanism has much in common with waves such as those commonly observed in the spread of an epidemie. A mollusc can enlarge its shell only at the shell margin. In most cases, only at this margin are new elements of the pigmentation pattern added. Therefore, the shell pattern preserves arecord in time of a process that took place in a narrow zone at the growing edge. A certain point on the shell represents a certain moment in its history. Like a time machine one can go into the past or the future just by turning the shell back and forth. Having this complete historieal record opens the possibility of decoding the generic principles behind this beauty. My interest in these patterns began with a dinner in an Italian restaurant.