We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident.
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