ART MATRIX PO 880 Ithaca, NY 14851-0880 USA (607) 277-0959, Fax (607) 277-8913 'The Paths of Lovers Cross in the Line of Duty.' THE THEORY BEHIND 'THE CELL AND THE WOMB' Recapture Copyright (C) 1990 by Homer Wilson Smith All Rights Reserved A Julia Set acts as a fenced in boundary to Z's starting off inside the Julia Set. Those starting off outside quickly go to infinity, and those inside quickly attain their stable periodic or chaotic orbits. Thus if a Z starts off inside the Julia Set it will still be inside after one iteration and closer 'in' so to speak. If a Z starts off outside the Julia Set, even by an infinitesimal amount, it will be further outside after one iteration. The question arises, what happens if C changes between iterations? The answer is quite simple. Lets say we start with a particular C with its Julia Set and a Z inside that same Julia Set. After one iteration of Z = Z*Z + C, Z will have moved to some other point still inside. If we now change C, perhaps by the equation C = C/2 + Z, then a new Julia Set will form in place of the first one. If this new Julia Set contains the Z point we just iterated, then the next iteration of Z using the NEW C will move Z to another point still inside the new Julia Set. If however the new Julia Set does not contain the Z, then the next iteration of Z will cause it to move to another point further away from the new Julia Set. Clearly with each change in C, the new Julia Sets either will or will not contain the previous Z. If they do contain the Z, the Z value will stay CAPTURED in the ever changing Julia Sets. Even if a few Julia Sets do NOT contain the Z, the Z will move away towards infinity but may still be RECAPTURED by further Julia Sets before it reaches a point of no return. If however a Z moves far enough away (point of no return), no possible Julia Set can ever recapture it and it will go to infinity and get colored. The Tarantula Rose, a movie on the video tape 'Mandelbrot Sets and Julia Sets' was made using just such an iteration. C is made to change after each iteration of Z making it very hard for Z to guarantee that it will stay inside the sequences of Julia Sets. In fact it is not obvious that any Z would ever stay captured at all. Only by looking at the computer pictures does it become obvious that life is indeed possible in a changing environment. Z stays 'alive' by NOT going to infinity which means it stays captured with in the reasonable bounds of the ever changing Julia Sets. Z = Z*Z + C C = C/2 + Z PAGE 2 This page left blank for your comments.