Monday, February 2, 2015

Extended Fibonacci and Fraction sets

This is one of the most amazing things I've seen yet, playing around with Extended Fibonacci. Many may overlook this because of all the numbers, but the results are...proof (?) of the fractal nature of the Golden Ratio. I've said it was fractal before, but it has been so difficult/daunting to place it within a context that can actually be seen.
I divided the 10 numbers as such:
1/3, 2/3
1/4, 2/4, 3/4
1/5, 2/5, 3/5, 4/5
The solution to each of these fractions, I did Fibonacci Sequence to.
Some fractions, of course, were duplicated. For example: 1/2 is the same as 3/6 4/8, etc. All duplicates were removed. Then, all fractions with their respective Fibonacci Sequence through f12 were placed in numerical order with the lesser on the left, and greater on the right.
When I 'folded' the entire table exactly in half, and added the overlapped numbers, it RECREATED THE FIBONACCI SERIES!
There are other awesome things going on in these tables. It is as if each fraction set of each whole number contains its own Fibonacci Set that is seen reflected in the original Extended Fibonacci Table. I wish there was a simpler way to convey this information!