Maximize resources

 

The CA is controlled by the following buttons:

Shorter: Makes CA shorter.
Longer: Makes CA longer.

Hide CA-2
Plant CA-1: CA-1 is planted.
Plant CA-2: CA-2 is planted.
ycoord CA-1 up: raise the site where the CA is planted
ycoord CA-1 down: lower the site where the CA is planted
ycoord CA-2  up: lower the site where the CA is planted

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

Before starting inspect the the previous two 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.

You may desynchronize the CA by replanting one of them. With time 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 while its resources = 20. This is not yet the final solution, but it will come.

This system is a non linear maximizer (optimizer)  with one maximum  {width = 24; resources = 20} which   has some interesting properties:

1. The two zygotes controlled by their rule = #600  generate a set of states.  The set is closed in the sense, that each of its members will converge to the one and only maximum{width = 24; resources =20}.  In other words when planting a CA you may choose a state instead  of the usual zygote and the outcome will be the same.

2. While   other artificial life constructs, e.g., neural nets, or genetic algorithms, converge to their optima asymptotically, here convergence is absolute.

3. Although the system is bounded it seems that the same holds also for an unbounded system.

4. As the system converges  its members become wider, and the probability p1 of resource accumulation rises.

5 As the system converges   movement of its members becomes more and more sluggish, and  their probability p2  to meet declines. Yet p1 increases faster than the decline rate of p2.