Process equation

A(t+1) = A(t) + g \sin(A(t))  \,.

Although variations of this equation have been studied before, Louis Kauffman and Hector Sabelli, thought that it modeled well processes in nature, and have named it accordingly.

When g is kept constant, then, depending on its value, this recursion generates either a steady state, periodicity, chaos, bios or infinitation (output increases in size toward infinity). When g = kt, where k is a small constant, this recursions generates all above patterns on different values of g. Without a conserved term, A(t), this recursion cannot produce bios. This recurrence relation is related to the circle map.

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