The challenge of irrationality: fractal protein recipes for PI

AbstractComputational development traditionally focuses on the use of an iterative, generative mapping process from genotype to phenotype in order to obtain complex phenotypes which comprise regularity, repetition and module reuse. This work examines whether an evolutionary computational developmental algorithm is capable of producing a phenotype with no known pattern at all: the irrational number PI. The paper summarizes the fractal protein algorithm, provides a new analysis of how fractals are exploited by the developmental process, then presents experiments, results and analysis showing that evolution is capable of producing an approximate algorithm for PI that goes beyond the limits of precision of the data types used.