Mathematical Building Blocks for Evolving Expressions

Gary R. Greenfield
Bridges: Mathematical Connections in Art, Music, and Science (2000)
Pages 61–70


We consider the problem of analyzing visual imagery obtained using Sims' method of evolving expressions from the perspective of the mathematical building blocks, or function primitives, that are used to form such expressions. We survey previously used sets of building blocks and then give the design principles and motivation for our latest set of such building blocks. This includes a new construction of building blocks starting from arbitrary continuous functions. We conclude by incorporating our building blocks into a coevolutionary system and show examples of images that emerged from the "primordial ooze" defined by our building blocks.