**Bounded chaos**

The CA is controlled by the following buttons:

**Hide CA-2
Shorter:** Makes CA shorter.

Information:

**Resources=** the amount of resources the CA has

**Ca width: **

**Infusion: **

**Before starting
inspect the previous experiments. **When the experiment
starts the two CA start moving. Their resources decline and they
get thinner when dropping below -40 (resources < -40) they turn
toward each other. When they touch or overlap resources are replenished
to a maximum of 20 and the CA get wider. Each CA senses where the
other is. Both bounce back from the borders.

First set infusion = false

You may desynchronize the CA by replanting one of them. The CA become
more and more attracted to each other, and their resources increase.
They become wider and their movement more sluggish. Finally they
take up the structure of the isolated (default) CA with resources
= 20. You may now replant them, and change their initial position.
The system will converge to the same final solution. It may happen
that a CA becomes wide and asymmetric and its resources = 20. This
is not yet the final solution, but it will come.

Definitions:

**Differentiation set**: Is the set of CA states which will converge
to a maximum.

**Differentiation trajectory**: The transition within the differentiation
set.

**Isolated CA**: Is the CA structure at maximum or its final state,
when the CA does not interact.

After the CA had reached their final states (both are isolated) **set
infusion = true**. From now on CA-1 adds one bit to CA-2 structure.
CA-1 structure is not affected. The system will remain at its maximum
(resources =20), yet CA-2 will behave chaotically. As long as both
CA touch each other, CA-1 will maintain its isolated structure, and
CA-2 will oscillate chaotically. It may detach itself from CA-1, whereupon
both differentiate and start moving toward each other. When you stop
the infusion (infusion = false|) both CA will settle at their maximum.

**Summary
**

Both CA reach their maximum.

1. Chaotic: as long as both CA touch each other.

2. Differentiation: When both CA are separated.

When infusion = true, the** system**
will oscillates between two attractors.

**Bounded chaos**

Here we have a chaos which does not depend on any initial condition,
since the process is continuous. It depends on both CA and is bounded.
All processes in our organism interact similarly. They interchange
resources, perturb each other, become chaotic and remain bounded.
Collectively they maintain homeostasis. (*papers complexity

p.s.

After stopping infusion CA-2 will start differentiating. Apparently
all the states traced during chaos initiate also the differentiation
trajectory. Yet they are obviously different from those of the
above defined differentiation set. We may call this chaotic set as
a potentially differentiation set, which seems to be the super set
of the above differentiation set.