Due to the previous discussion “Fibonexus”  I began exploring ways of achieving the Rodin nexus key using the Fibonacci sequence.

The three possible mod9 nexus keys are.
: Sequence 165297438834792561
: Sequence 231495867768594132
: Sequence 173553719816446289

As was pointed out, Fibonacci numbers can be divided into smaller Fibonacci numbers and whole integer results can be found at regular intervals in the sequence. For example every seventh Fib number will divide into Fibonacci number 13. I charted all the results of these divisions, and reduced the results to mod9, mod25, and mod49. Once repeating patterns were found for each moduli, no higher Fibonacci / Lucas numbers were explored.

Fibonacci divided into Fibonacci numbers reduced to modulus 9 are shown in the first file: fib divided by fib mod9 DATA.pdf
Quite simply every fib number is tabled down the vertical axis of the table. The divisors are arranged across the top axis. Every number that will divide into a Fibonacci number and remain whole is shown – reduced to mod9.
I noticed every sequence for each divisor, going down through the table is very specific and has a repeating pattern.

I created a second set of data in Lucas divided by lucas mod9 DATA.pdf

I summarised the (repeated) sequences of both sets in the third file: Mod9 ANALYSIS.pdf

This allows us to see more clearly the specific mod9 sequence that applies to each divisor for both Fib and Lucas. There are many interesting things about this groups of sequences, many noted below the table. However for now the key thing is this: Notice that the 18 digit sequences are all the same in the Fibonacci group, are attributed every 8th sequence beginning with sequence 4, and are all identical. They form the Rodin Nexus Key for one of the 3 Rodin number maps – to be found at the end of the document. So where could I find the other two nexus keys that applied to the  and the  Rodin maps?

For the Lucas group there is an interesting pattern to the sequences, noted below the table. Here the nexus key occurs with greater frequency: Every 4th sequence beginning with sequence 2 forms the 18 digit Rodin Nexus Key that makes up the  Rodin number map
Making the  Rodin Map is then fairly easily deduced from this data as shown in the notes.

I have also data for Mod25 and Mod49. I have found the Nexus keys and therefore number maps for each of these. the files relating to them I will upload as soon as I can.

I checked Mod16 to see if there was anyway to achieve a number map with this. No luck. I have the data available for this too, and will post when it is possible to upload more MB’s.

I am now in the process of checking Mod81, which Randy Powell states there is no workable map for. I believe him, but I just need to check for myself to ascertain exactly why.

If anyone spots any mistakes in any of these files please do let me know. Otherwise I hope they are clear, and not too laborious to look through.

I have found that there is plenty more analysis and insight that can be put into this data. However I need to move on to other things, and I just wanted to post this stuff to be able to share it with people.

Kind regards,

Tom

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In extension of this phi research:

I have been trying to ascertain for some time what proportions a VBM torus should be. Randy and I have had many discussions, and tried a whole variety of ideas, making visualisations in 3d to see if resonances that accord with the simplicity of the maths can occur.

I have found one way of applying proportions to tori of different scale maps that accepts one rule as it's premise. It is a mathematical experiment which leads to a very specific conclusion. But I am not trying to promote this as THE solution to the proportions issue. But these Tori fit nicely together with totally exact phi ratio proportions, and this has a certain beauty to it which is worth checking out in any case. Its only in mod9 at the moment, so I will need to check mod25 and mod49 sometime. But I tried so so many calculations before landing on phi as the being the correct proportions.

The rule? This is that each diamond on the grid surface of a torus should be equal in surface area to every other diamond. And in every torus (all of which layer up with an onion skin/russian doll effect resembling the electromagnetic field of a planet) this diamond area will always remain the same.

check out some of the data here:

http://vortexspace.org/display/~tom+barnett/Phi+VBM+Tori+Discoveries

T

25,49,121,…..

the ones that will work will be prime squares, maybe even cubes?

here is a list of what might work, 25,49,121,169,289,361,529,625,841,961,1225,1369,1681,…...

1/4(6n-(-1)^n+3)^2 is the equation that will generate this sequence. 744711744711744711

Notice that each number you listed above (25, 49, 121, 169, etc...) is a multiple of 12, + 1.  Your formula above is also centered around 6n.  6n (+ or -) 1 produces a set of numbers containing the set of all prime numbers.  All primes in hexadecimal end in 1 or 5, and all primes in duodecimal end in 1, 5, 7, or (11).  It is useful to look at this stuff in base 12. In addition (pardon the pun), the 24 digit repeating pattern in the Fibonacci series in base 12 (I am using "a" for 10 and "b" for 11) is 0,1,1,2,3,5,8,1,9,a,7,5, and the second half -- 0, 5, 5, a, 3, 1, 4, 5, 9, 2, b, 1.  Notice that the only number with which no Fibonacci number ends in base 12 is 6, however superimposed and added together (which would be the same as writing the digits in a circle and adding together the numbers positioned opposite to each other), the first and second half form the pattern 0, 6, 6, 0, 6, 6, 0, 6, 6, etc... 