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RADICAL NEW BRAIN THEORY

  I have come up with a very interesting new theory on the way the brain
  represents spatial patterns by  way  of harmonic resonant interactions
  between electrically coupled neurons.  The big advantage of using such
  resonances is that a simple  physical system, for  example a bell,  is
  capable of responding to and reproducing fantastically complex spatial
  patterns, i.e.  the  harmonics of  the  bell,  in a remarkably  robust
  manner  using  simple dynamical   interactions, and  can encode  those
  complex spatial patterns  in a simple and  highly  compressed rotation
  invariant code, i.e.   the  oscillation frequency corresponding to the
  harmonic pattern.   This is a radically new  theory, and  suggests  an
  entirely new  mode of communication between neurons  in the  brain.  I
  have performed a number of  computer simulations which  have confirmed
  the validity of the theory by accurately reproducing a large number of
  visual phenomena by way of a single simple mechanism.

NEED REFERENCES ON SPHERICAL HARMONICS

  I would now  like  to  extend  the orientational  harmonic   theory to
  explain three-dimensional harmonics, in order  to explore the kinds of
  spatial structures that can be represented by this kind of system.  In
  order to do this, I  need to  read up on  spherical harmonics.  I have
  found a number of books in the library full of fantastically elaborate
  differential equations, etc, but  that is  NOT what  I am looking for.
  What I want is either a catalogue of the kinds of patterns represented
  by the  first few harmonics, or  a SIMPLE description  of  how I could
  write a computer program that would reproduce these patterns.

  For  example, some  astronomy books explain  how the sun is constantly
  oscillating, or ringing like a  bell, and the fundamental harmonics of
  these oscillations include:

    bulging all over, then shrinking all over, alternately

    bulging in the northern hemisphere while shrinking in the
    southern, and the inverse, alternately

    bulging  at  the equator  and   shrinking  at the  poles...

    bulging at the equatior and at a northern and southern "temperate"
    lattitude, while shrinking elsewhere...

    etc, etc...

  in  other words, this    set  of   harmonics  defines  a   series of
  alternating subdivisions   by lattitude.  Another  set  of harmonics
  defines  a  similar  alternation by  longitude, creating alternating
  "orange  slices".  Combinations of  these  two modes of  oscillation
  produce checkerboard patterns, and so forth.  Each of these patterns
  corresponds to  a   particular  temporal  waveform  or   oscillation
  frequency  which  therefore represents  that  pattern  in a rotation
  invariant manner.  The bizzar patterns seen in electron orbitals are
  yet another example of spherical harmonics.  Does anybody know  of a
  reference that  would list  these different pattern  types, or  give
  equations that are  simple enough that  I could   type them into  my
  computer and generate families of  these  patterns  myself?  I  have
  neither the inclination nor the ability to plummet the depths of the
  differential equations defining such systems, I only want to look at
  the resultant patterns.

  Can anybody out there help me?
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