Mathematical bios

In this paper we report on a mathematical pattern that we call bios, and its generation by recursions of bipolar feedback. Bios is a newly found form of organization, that resembles chaos in its aperiodic pattern and its extreme sensitivity to initial conditions, but has additional properties (diversification, novelty, nonrandom complexity, life‐limited patterning, 1/f power spectrum) found in natural creative processes, and absent in chaos. The process equation A_t+1=A_t+g_tsin(A_t) generates convergence to π, a cascade of bifurcations, chaos, bios and infinitation, as the value of the feedback gain g_t increases. In the complex plane, series generated by orthogonal process equations display fractal organic patterns.