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And now I reward your patience for these outrageous ideas and propositions by coming to the last diagrams. I call them the "Main Sequence" which follows the production of new relationships under the process of 'symmetry breaking', and the "Main Curve" which specifies how a gaussian-bubble system handles information and energy, indicating how real dynamics and optionspaces are dealt with. I leave you to explore both of these on your own.
The Sequence simply shows how Apollonian relationships arise out of symmetry breaking (adding dimensions) and model quite exactly the exposition of the fundamental forces. For example, it indicates that the "Monopole" state of electro- magnetism (EM) is the full Apollonian Circle in 2-dimensions only. A 'monopole' is not simply one-half of a 3-dimensional EM dipole. It is something quite condensed relative to the Dipole configuration.
The topology of existence is a fully connected self-sensitive architecture, with vast pluralities of interacting systems, each with their own gradients of changing entropy and negentropy dynamics, the essential qualities of which are explored relative to the simple Gaussian "Main Curve".
Systems tend to be environmentally sensitive and therefore have to be evaluated as having broad and competent behavior ranges rather than the skittish balance nodes depicted by Complexity/Chaos theory and fractal dimension algorithms. That is, all systems have the apperance of being "closed and well bounded", when in fact, they are open. Under this model of open dynamic interactions , the most stable and long lasting systems are not necessarily those which are rigidly fixed and impervious to encounters from 'external' sources, but those which have the ability and internal openness to absorb more energy or information, process it, and still remain functionally competent. Complexity therefore is the increasing capacity to encounter and handle more and different kinds of interactions .... survive, and even improve those capacities via adaptation and other mechanisms - including emergence .