Let’s examine some properties of bounded chaos. CA-0 is periodic, and CA-1, chaotic.
The next graphs depict their return maps. The experiment was terminated after 500 time units. If we would continue, the map of CA-0 would remain the same, while the CA-1 plot would be filled with new dots.
Despite its apparent simplicity the CA-0 map poses some difficulty. Several points are aligned along vertical lines, which means that the mapping from velocity[now] to velocity[next] is not one to one, but one to many. In other words, neither the return map, nor the phase space provide enough information for reconstructing the velocity trajectory and more information is needed. Since CA-0 states are discrete and finite this information may still be gathered from other CA-0 attributes.
A similar mapping of CA-1states does not exist and the map is chaotic. Nevertheless it reveals an important property, CA-1 states are bounded. CA-1 oscillates within a boundary known as a strange attractor. One wonders how does such a boundary arise? Most famous attractors, like Lorenz’s are generated with a few differential equations. They are top-down attractors controlled by a central agency. The CA-0 attractor on the other hand, is determined by the periphery, or the CA-1 context which changes from state to state. Context determines the CA-0 boundary.
Wisdom of the Body (WOB)
Two kinds of transformation advance a CA from state to state. Transformations defined during model design, and those determined by the ever changing CA context. The latter are extremely complex and cannot be expressed with the available mathematical tools. They are called here WOB transformations. WOB emerges with the proliferon. Here we search for proliferons which settle at solutions or strange attractors.
The weather system also consists of many local states whose transitions are determined by their contexts. However, Lorenz’s model is too simplistic to account for these intricacies. Above all it does not rely on WOB transformations. Its strange attractors drove Lorenz to strange conclusions, like the butterfly effect according to which a butterfly flapping it's wings in one area of the world may initiate a storm elsewhere. The weather system is a manifestation of Gaia, whose main property is a bounded chaos. If it would not be bounded it would have escaped into the outer space long time ago. Each state of the weather is a Gaia solution. Gaia and its weather proceed from solution to solution. Its essence is inertia which resists the flapping of butterfly wings. At best a butterfly may (humbly) join the context of a weather state. The Butterfly effect is an artifact of a centralized model which barely accounts for the intricacy of a weather system.
Since WOB cannot be expressed with the available mathematical tools, it has to be searched for by trial and error. You design a CA system and hope that it will manifest the kind of WOB you are searching for. Gone are the days when mathematicians searched for hidden laws in Plato’s heaven. The future of mathematics is system breeding. What about medicine? We are fortunate that our organism is controlled by WOB, which drives it from solution to solution. All that is needed is to understand WOB ways and messages. This is what the New Kind of Medicine is about.
“You never step into the same river twice” said Heraclitus, to which we added “ you never meet the same individual twice”. Does it matter? Not at all, since despite the fact that an individual continually changes, you still recognize him. His chaos is bounded, and the boundaries are controlled by WOB.