**Natural Fractals for 3 and 4 Dimensional Pathways**

*21 April, 2013*

**L. Edgar Otto**
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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