Sunday, April 21, 2013
Natural Fractals for 3 and 4 Dimensional Pathways
Natural Fractals for 3 and 4 Dimensional Pathways
L. Edgar Otto 21 April, 2013
By "natural fractal" I mean a pathway described by a simple right angle 24 combinatorial elements describing the rigid rotation of a cube. The lattice contains 24 elements of 6 directions depending on the orientation of the identity and there is assumed 5 of six directions for motion from an initial location. In four dimensions an analogy exists of the 120 elements of the dodecahedron for a higher lattice as such.
The choices of orientation and direction may not correspond in free descriptions, locally, to that of the factoring of natural dimensions where they are prime number entities.
The looping ensemble at points in a graph is in a sense the question of a free extension over n translation same direction steps presumably limited by general ideas as to the intelligible relations between such abstract geometric entities.
I am not sure if this is the standard way among choices such fractals are done or programmed. For a standard among choices I set the last arrangement of the symmetry notations by the last model I assembled regardless of spin directions and overall chirality and mirrors in the now explored case of three space. The sixth face or last face of a cube assumes but five colors as if it empty or difficult to assemble as if negative if we designate an unique frame of an implied adjacent dimensional point in its interior quasifinite variations for multiplicity and connectivity.
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Inversions are all important where at each node or rest point one of the six colors itself contains sub fractal abstract motions otherwise we simply designate the color out from thru the three natural axes. But as if this ground a mirroring it also can ground the idea of vibrations in inversion duality but with respect only as one side of higher abstract mirrors. In effect we describe motions as some combination of identity, reflections, rotations over an orthogonal or simplex group where the idea of rigidity can have wider variations.
By such a method we can make more intelligible in a positive direction within a natural four base the chromatic or twelve base information entities.
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Equivalently we can regard such a fractal path thru three space as a combination of emphasized or privileged complex systems in tandem with a duplication of the system as well as only taking half values of the real parts. But the idea of extension into binary and bilateral n-dimensional symmetry as virality admits half values of the totality of systems as if a reflection or image not necessarily real. Can we extend this paradox to finer detail and richer systems of space or symmetry operations beyond mere duplication or halving of these null or dimensionless contexts of abstract motions that fundamentally describes and makes unique in choice the span of quasic generations or the particle generations including regions or holes, vacua left as if in the landscape broken from a period of glaciation part of the buried ice melts to leave a kettle lack as the world warms?
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More detailed explorations will appear here with more formal illustrations. This would be a good programming project in which we may enumerate possible paths as information theory. This could include probability methods for those so inclined.
Can we by methods close to or beyond absolute zero achieve what we want to find by greater ideas of heat where they apply to quasinfinite flat or round surfaces such as that thought for the physics of black holes- and would this not take a new vision from a deeper concept than mere extension of our ideas of new symmetry operations?
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I got up early and watched a general statistics course on PBS from Stout University. I was general but an area I may have thought about but not in those terms other than say the general bell curve. This evidently is the main method for sociological data analysis and some ideas were said relatively new, since the 80's. I found many things wrong with the general ideas that could easily be resolved if we resolve the questions of the infinite and finite, in particular the idea of unity and a deeper role for counting as a principle that is not only easy to understand but in context is certainly more foundational.
Specifically, although I see some researchers pushing the envelop in statistical methods and analysis, that the idea of Bayesian statistics in that it is a continuous development is weak on that very point. What I observed or found perhaps by talking with others, with students, is that their expectations were colored by this general method that certainly should not be one that uses count in a non-mathematical way to promote aspects of teaching. A true inquirer should not just appeal to one side of ideas to which he sees as the grounding with some degree of certainty so parrots his larning. This appeal to nominal-ism is quite an antithesis to radical empiricism. Indeed, how far are we certain in our Bayesian measure before even the physicists lose interest and the subject vanishes beyond expectations and observation, or the question in retrospect no longer applies once we have reached a higher level of intimate and non-local connections transferring information if not signals. But I did see hints of directions in deeper areas in which I think we all seem to be heading.
Pardon me if anything I write has come from such secondhand rumors, damn rumors, and statistics. Time has not moved on so much as piled higher and deeper.
Is it not very basic in four space a worm, or a hole it makes, eats the volume comes to the surface and eats as much again? This the beginning? In any case variance (which Bayes was wise to publish after his death but the lecturer did not seem to know why, after all could God make Bayes irrelevant like some physics without Bayes?) So if I have used that vocabulary (not terms, teaching not usually as high a pursuit in today's universities) variation in the statistical sense then I caution it may have other legitimate fields senses, such as the temporary general structure of co-variance... In any case in multivariate could we not have a fractal like situation where it makes sense with care to widen the conditions and parameters as well the correlations?
I will explore and post later on the fractal path ideas but I will post some casual drawings that seem to relate to the themes at hand.
In an abductive world, and a quasifinite one with a more general idea of holographic boundaries, clearly we may consider half a four dimensional apple as well as half a worm... in the ranking methods of statistics there is a caution to put the unity or one at the top rather than multiplicity of values at the bottom- abstactly, this is the grounding of total or totally divergent theories, of everything.
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