Monday, April 7, 2014

Fibonacci Packing

Wiki talks about it here. The reason I bring it up is because I think that is how things get packed, like in the proton. In the vacuum, each of those digits, below,  is itself a Fibonacci packing of a lower order.  Stability, or the probability of one 'digit' decaying into another is related to the sparsity of the packing. I bring it up because my colliditron has to show why the proton is so stable when the neutron is not. These particles sit way up in the order, and beyond them the next Shannon equal integer is some (3/2)**600 beyond, way beyond the precision of my spreadsheet.  The coding below is why I think the sample rate of phase is the Fibonacci ratio.  But, the real triumph will be if my quantizing macro can differentiate create both the proton and neutron. If so, then the output calculations of Shannon overlap must show the extreme stability of the proton. I hope.  Anyway, I am stepping thru the quantizer, things are going well.

Symbol Fibonacci representation Fibonacci code word implied distribution
1 F(2) 11 1/4
2 F(3) 011 1/8
3 F(4) 0011 1/16
4 F(2) + F(4) 1011 1/16
5 F(5) 00011 1/32
6 F(2) + F(5) 10011 1/32
7 F(3) + F(5) 01011 1/32
8 F(6) 000011 1/64
9 F(2) + F(6) 100011 1/64
10 F(3) + F(6) 010011 1/64
11 F(4) + F(6) 001011 1/64
12 F(2)+F(4)+F(6) 101011 1/64
13 F(7) 0000011 1/128
14 F(2) + F(7) 1000011 1/128

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