Strange attractors

Previous experiments explored mutual stimulators. In the present experiment CA-0 (stem process) continually stimulates CA-1:
delivery: [1, 1, While[p[1] > k], 2]; {k, 1, 50}
augment state: [state[1, i+1] += state[0, i], While[p[1] > 0]

The proliferon is exposed to a continuous demand by the environment rising from 1 to 50 relative resource units. (v. Chapter-107, Chapter-108, Chapter-109). The outcomes are bounded chaotic CA which oscillate in a bounded region of a strange attractor.

Initially the CA are overwhelmed by the demand and their resources are depleted. As demand rises they become more vigorous, produce more and their health improves

 Bounded chaos

Hitherto chaotic outcome was avoided since chaos is a threat to the proliferon and may kill it. Bounded chaos however does not pose any threat to the proliferon and will also be regarded as a solution. Many oscillators operate in our body, some display diurnal rhythms, while most oscillators are chaotic strange attractors.

Bounded logistic system

The logistic map: x[n + 1] = r*x[n]*(1 x[n]) exhibits a similar relationship between periodic oscillators and chaos. As r increases from 0 and upward the logistic equation settles at solutions whose period depends on r. Approximately beyond r = 3.57 most solutions are chaotic and unbounded. From the present perspective the logistic equation is a non interacting isolated process. It might even be represented by a CA. Once interacting with other processes (the environment) some logistic maps might settle at a bounded chaos.

delivery: [j, j-1, While[p[j-1] > set point], 2]
First argument: CA receiving the delivery.
Second argument: Delivering CA.
Third argument: Delivery condition.
Fourth argument: Delivery amount.
p[j]: daily production.

augment state: [state[j, i+1] += state[j-1, i], While[p[j-1] > p[ j ]]]
First argument: state augmentation.
Second argument: Delivery condition.
p[j]: daily production.