Strange attractors
delivery: [1, 1, While[p[1] > k],
2]; {k, 1, 50}
augment state: [state[1, i+1]
+= state[0, i], While[p[1] > 0]
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
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.
First argument: CA receiving the delivery.
Second argument: Delivering CA.
Third argument: Delivery condition.
Fourth argument: Delivery amount.
p[j]: daily production.
First argument: state augmentation.
Second argument: Delivery condition.
p[j]: daily production.