Bounded chaos

The CA is controlled by the following buttons:

Hide CA-2
 Makes CA shorter.
Longer: Makes CA longer.
Plant CA-1: CA-1 is planted.
Plant CA-2: CA-2 is planted.
Infusion: CA-1 adds one of its bits to CA-2, which happens only when they touch each other.

Resources= the amount of resources the CA has
Ca width:

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.

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.


infusion = false:
Both CA reach their maximum.
infusion = true:
CA-1 will always trace the differentiation trajectory, and attempt to reach its maximum which it can maintain only  as long as both CA touch each other. Once they are separated, it will start losing resources and attempt to interact with CA-2.
CA-2  will proceed along two trajectories:
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


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.