Free will

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.
width CA-1+: Make CA-1 wider
width CA-1 -:
Make CA-1 slimmer
width CA-2+:
Make CA-2 wider
width CA-2 -:
Make CA-2 slimmer

the amount of resources the CA has
Width: CA width

Before starting inspect the set of movement solutions . When the experiment   starts the two CA (width =12) start moving . Their resources decline and when dropping below -40  (resources < -40) they turn toward each other. When they touch or overlap resources are replenished to a maximum of 20.  Each CA senses where the other is. Both bounce back from  the borders.

Watch for a while then desynchronize their actions by planting a CA. Then start narrowing their width, When wider than 12 the CA structure becomes chaotic and when width=24  (default isolated state) it stops moving. Here are some recommended experiments:
1. CA-1[width =2] CA-2[width=6] You will note that CA-2 is influenced by CA-1 decisions. Now plant CA-2
2. CA-1[width = 16 ] CA-2[width=4] Hide CA-2 and watch CA-1.  Despite being sluggish, whenever resources drop below -40 it will seek  the other CA.
3. CA-1[width = 24 ] CA-2[width=6] Plant CA-1. It will stop moving and control CA-2

Now forget the underlying rules that drive the system how would  you interpret its behavior?


When width <=12,  the CA behave like an oscillating planetary system. Their movements might be approximated by noisy  Newtonian dynamics.

1. In reality  no noise is involved neither here nor in all other experiments.
2. Action-at-a-distance interactions, e.g., gravitational or magnetic, is  not implemented in the program. Here you have a system in which the second and third laws of motions are not operating. Only the first, the CA proceeds in its motion until ‘deciding’ otherwise.

While in Newtonian systems the particle is passive, here it ‘decides’.  Now imagine a new kind of mechanics which allows the particle to decide, and  contains Newtonian mechanics as a subset where particles do not decide.  The superset might be the mechanics of life while the subset, of physics. Such contemplations illustrate the merit of the present experiment. It  stimulates your thinking

When width >= 16 the CA behaves chaotically. Yet since it is not sensitive on its initial conditions  is it really chaotic?  Here we need a new kind of chaos definition, bounded chaos Now regard the system as a whole, including both CA. Its center of mass occupies a strange attractor.


When the CA resources drop below -40, it ‘realizes’ that it has to seek its neighbor. It responds somewhat later as if deciding when to turn. Which illustrates that in this fully deterministic system a constrained free will is still possible.  After all  our free will is also constrained, e.g.,  by gravity.


The two CA illustrate the behavior of a married couple. Their relationships fluctuate  between mutual attraction and repulsion, which neuroscientist  might  attribute to their mutual dopamine levels (resources = dopamine level). Or might the present system simulate bipolar disorders?