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(t) sin(A(t)) generates convergence to pi, 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.