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First, there are several cases where the NKS book introduces what was, during the book's composition, the simplest known system in some class that has a particular characteristic. Some examples include the first primitive recursive function that results in complexity, the smallest universal Turing Machine , and the shortest axiom for propositional calculus . In a similar vein, Wolfram also demonstrates many simple programs that exhibit phenomena like phase transitions , conserved quantities , continuum behavior, and thermodynamics that are familiar from traditional science. Simple computational models of natural systems like shell growth , fluid turbulence , and phyllotaxis are a final category of applications that fall in this theme.