Saturday, March 15, 2008

Visualising fractal dynamics

Fractal dynamics, the communication between the macroscales with the microscales. In the 'Mind and Brain, Chaos and Quantum Mechanics' paper, page 19, I read:

"The dynamics of many important biological molecules may be fractal in this way, which involves the linkage between a variety of quantum excitations of differing energies, and feedback between tertiary structures and active sites."

Communication of higher scales with lower scales. In this example the higher scales being the tertiary structures and active sites of biological molecules and lower scales being the quantum states of the atoms of the biological molecules.

Quantum excitations of differing energies of the atoms of the biological molecules linked with the tertiary structures and active sites of the biological molecules. As the active sites of the biological molecules define the function(s) of the biological molecule and by that the function(s) of the cell organelles it is part of, the higher level of organised matter.

Different levels of matter organisation, fractally connected.

"... structures behaving, not only in a geometrical sense, but also dynamically ..."

Fractal dynamics surpass in breadth and depth, vertically and horizontally, all aspects of human activity among many other aspects of reality. And in each level of organised matter established attractors, a range of stable states as they are defined by optimally maximised local variables and parametres. Such attractors in turn by virtue of the fractal connections determine the establishment of attractors in higher levels as the local variables exert an influence on global variables and parametres.

And since the fractal dynamics provide a two-way path and local variables are influenced by global variables in turn, it leads to the establishment of new attractors by chaotic bifurcations.

If however global variables induced adjustment of local variables and parametres requires tweaking of variables and parametres outside the limits permitted by the local system, the local system will cease to be.

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