Check this out! The fibonacci sequence;

#, Full Value, Decimal Parity Value 

1 1 1
2 1 1
3 2 2
4 3 3
5 5 5
6 8 8
7 13 4
8 21 3
9 34 7
10 55 1
11 89 8
12 144 9

13 233 8
14 377 8
15 610 7
16 987 6
17 1597 4
18 2584 1
19 4181 5
20 6765 6
21 10946 2
22 17711 8
23 28657 1
24 46368 9

25 75025 1
26 121393 1
27 196418 2
28 317811 3
29 514229 5
30 832040 8
31 1346269 4
32 2178309 3
33 3524578 7
34 5702887 1
35 9227465 8
36 14930352 9

37 24157817 8
38 39088169 8
39 63245986 7
40 102334155 6
41 165580141 4
42 267914296 1
43 433494437 5
44 701408733 6
45 1134903170 2
46 1836311903 8
47 2971215073 1
48 4807526976 9

It repeats fully in lots of 24 or half in 12! 

It's more obvious if I re-number the positions by 12's. (btw, 12 is a second generation 3)

Just match the positions and observe the symmetry around 9 once more...

1 1 1
2 1 1
3 2 2
4 3 3
5 5 5
6 8 8
7 13 4
8 21 3
9 34 7
10 55 1
11 89 8
12 144 9

1 233 8
2 377 8
3 610 7
4 987 6
5 1597 5
6 2584 1
7 4181 5
8 6765 6
9 10946 2
10 17711 8
11 28657 1
12 46368 9
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
1 75025 1
2 121393 1
3 196418 2
4 317811 3
5 514229 5
6 832040 8
7 1346269 4
8 2178309 3
9 3524578 7
10 5702887 1
11 9227465 8
12 14930352 9

1 24157817 8
2 39088169 8
3 63245986 7
4 102334155 6
5 165580141 4
6 267914296 1
7 433494437 5
8 701408733 6
9 1134903170 2
10 1836311903 8
11 2971215073 1
12 4807526976 9



It's hard to display in this forum setting but hopefully you can see what I am doing here.

The decimal parity reveals the harmonics and the harmonics repeat every 24 positions.

__________________
Squeegee your third-fucking-eye-(Bill Hicks)

......and guess where the phi ratio is found...... take the last Fibonacci number of 24 and the 1st number in the next section of 24 and divide the last with the first;

46368 divided by 75025 = 0.618033988.......

Or the next 24 position scale; 

4807526976 divided by 7778742049 = 0.618033988........

If I replace the numbers with their compressed versions you have 9 divided by 1 = 9 therefore Phi = 9 


You'll also notice that in the first group of 12 there are 2 threes and no sixes. And in the next 12, to make 24, there are 2 sixes and no threes.

And of course 12 is 3 and 24 is 6.

Now, if you add up all of the compressed numbers, from position 1 to 12, you have = 52 which equals 7
And if you add the next 12 up, positions 13 to 24, you have = 65 which equals 11 which is 2

2 & 7 = 9

__________________
Squeegee your third-fucking-eye-(Bill Hicks)

Last one for a bit I think....

I reran the Fibonacci Sequence reordered to only 9's, but kept your simplified numbers. Some very interesting patterns emerge. I broke these into groups of three, and separated out a sequence that broke the mirroring. I am not sure what this indicates, but it is interesting that it is the 4th groups. Based on the sequence of 12, this is the odd ball grouping. It does make me think there is something more going on with angular momentum, as mentioned above, the 120º reduces to 40º - which is 4. I am going to play with some numbers on this, as this seems to have some interesting correlations.


In looking at the patterns that emerge in this sequence, there is tons of repetition everywhere. Interestingly, the repetitions only seem to flow in one direction. There are a few exceptions, but there seems to be many mirrors in going predominately only one direction.

I had to stop this thread in mid-thought to recreate the sequence with different coloring. I think if this sequence was extended out for quite some distance, there would be some repetitions. I have a feeling this would equate to a full "swirl" of the Fibonacci Spiral.

Here is the modified sequence:


I tried to highlight some various elements, but the colors are probably a bit hard to discern. The first series of patterns in the first column is the red number patterns (1-1-5, 3-8-8, 4-6-1). These can be seen echoed all through the grid, most of them are offset and cross multiple grids. However, they seem to stay in nice convenient 3X3 patterns. Follow the 1-1-5 sequence down the first column and see it starting at row 7. The following two number groups are in sequence with it - even though it is offset by 2 numbers and spans two columns.
The same sequence can be seen going vertically too. Look at the 1st 3X3 grid again, and trace the number patterns 1-1-2, 1-8-9, 5-6-2 all through the grid at the same sequence.

Anyway, lots of interest in this grid, and I think if it were extended out until ti repeats it would be interesting to see what exactly we are looking at. I may play with this, but this is getting off topic of what I was working on, so I may not play with this much further. This is definitely full of symmetry, and can be seen in almost every facet of this. I think this further emphasis the perfection of this sequence and shape, and converted to Marko's Vortex Math system, really provides some credibility for both systems.