Phi VBM Tori Array




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Published on Feb 13, 2013

Music by Simon Mathewson
Hear more of his tunes here: http://freemusicarchive.org/music/Sim...

This film presents recent research, insights, and ideas linking the divine ratio or Phi, and Vortex Based Mathematics.
It begins by showing how the Modular 9 VBM maps can be derived from the Fibonacci sequence. VBM maps in Mod 25, mod 49 and so on can also be found using the fibonacci sequence, and the lucas sequence. The data behind this information can be found here:


The film then go's on to explain some of the established compelling number properties of the mod9 number maps.

Then the problems that have been identified concerning the proportions and configuration of the VBM tori are explained.

I then propose a possible solution to these problems that also encompasses the Phi ratio. This solution involves laying down one specific geometric rule: That each diamond on the surface of the torus have exactly the same surface area.
My finding of the phi ratio was purely accidental. I had been looking for any proportion which allowed for this rule. I tried many different ratios of inner to outer diameters before landing on phi.

I am an artist, not a trained mathematician, nor a programmer. There could well be some mistakes in my calculations. If so don't hesitate to let me know, and I will update the video.

There are definitely inaccuracies in the visuals depicted, as I have relied on drawings to define these new maps. I have calculated the 9x36 measurements slightly more precisely that the video. I will be attaching a cross section of this tori so that electronic engineers (perhaps those who have already created abha coils) might be able to manufacture a coil with these proportions.
The cross section is also here: http://www.tombarnett.net/vbm

If any electronic engineers or CG programmers would like to help continue the research here please get in touch.


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