![]() |
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.