**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]

**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.