Process equation

: $A(t+1)\; =\; A(t)\; +\; g\; \backslash sin(A(t))\; \backslash ,.$

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.