Sunday, September 28, 2014

Wythoff arrays can pack sphere

Here I am working with a rational ratio and arranging packs of quants thare are  exponents of that ratio= r. I am limited to two a few exponents at any level of the sphere, and I have to be hyperbolic.  The circles sum the (1/r) and outside the circle I have motion as r So I have the worm gear evvect, the circles are tracking sum (1/ratio) = 1 and exchange r with the exterior. But volume to area reaches a critical point going from the perimeter to the center, so I jump to the next row of the Whythoff array:
 Anyway, this is where I am at.  I got here my messing with recursions and discovered the Wythoff did that for me.  The balance is matching motion and unit circles going toward the center, and switching to the next row at the critical moment.  The Wythoff work because they are minimally redundant, one can make the most quants with the least redundancy. Hyperbolics and finite differences and finite sums of local aggregates are the way to go.

So, all you sphere packers, carry on! I am trying to stop this, really, but it has become a sort of fun compulsion.

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