Vortex Based Math

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I thought I'd start this thread for all our Phi related findings, of which I have been finding a few lately. As soon as I started using powers of Phi, I found many things.


One of which is this;So the middle of a line which is sectioned 1.618, when a circle from the centre to the Phi point is scaled up by cubed Phi (4.236), defines the full line diameter.


What I was, and am looking for, is the connections between Phi/powers of Phi and doubling/halving/powers of 2. I believe that these two functions are recipricol in some way and are both exremely profound ratios. Phi, I believe, is the key to the torus shape and the fractal torus skin iterations/macro-micro expansion contraction...whereas the 64 Tetrahedron grid/Flower of Life/doubling-halving/powers of 2 are all about the sphere - a container, a matrix, a boundary....


I was particularly interested when I found this correlation between the flower of life/vesica/doubling-halving and CUBED Phi, because I am looking for 3D scaling. For instance, as Walter Russell points out also, to make a new "1" (sphere) you need 8 parts, as in, the seed of life in 3D is 8 spheres creating a new equalibriam, or 8 Tetrahedrons (Star Tetrahedron).  (1,8,1,8,1,8) (1,8,64,512,4096,32768)


1 and 8 are recipricol in the sense of cubing and are of course mirror pairs (the 2 directions,+/-, on a single axis). I have a strong feeling that this is why, when the Fibonacci series is compresed to single digits, and the VBM circuits are found, there are 2 doubling/halving circuits (in opposite directions, one emanation/spirit circuit and an extra circuit of 1,8,1,8,1,8 that mirrors the emenation circuit. So it is similar to the emanation circuit in some way... I have a feeling it has something to do with a dimensional scaling axis (macro/micro).

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ok, not Phi, but since this sequence is a cousin of Phi / fibonacci, I'll just put this here, brief introduction to the sequence here:




So this sequence creates a spiral of equilateral triangles, but apparently there is more to it. Looking at it 3d we can also see it also dealing with squares and cubes :) As we know equilateral triangle can be found inside the cube. I found this quite fitting since the sequence is based on cubing. Most simple example of this is to take a calculator and start with 1 take a cuberoot of that +1 take a cube root of that and repeat until you get closer to the value.. same works for phi, but you take a square root instead.. ;)


PS. Image courtesy of wolfram demonstrations.. I've only drawn on top of it to show the relevance better..


btw, what just occured to me is that phi is actually a  1-dimensional spiral inside a 2-dimensional plane. At the same time, padovan sequence is all that, but it is also a 2-dimensional spiral (drawn by equilateral triangles instead of just lines) inside 3-dimensions. How cool is that? :) so my next question would be, what does a 3d spiral inside a 4d-plane look like.. :-o  .

I dont really know what ya mean JT. How do you mean 1 dimensional spiral? And isn't 4D a motion?


@ Riseball - Could you give us a bit of a explanation of your images? Cheers.

sorry for my bad analogy, I meant to say that each component of the spiral has a 1d structure (line) inside a 2d frame (square)..the padovansequence has all the parts of a phi spiral (line & square), but top it off it has the 3d component of a cube.. so it has all the parts of previous structure and building on that... as for 4d, not sure..

My apologies, I know the FIBONACCI sequence is not quite the same as PHI, but the two go hand in hand together.


@Barbitone, in AutoCAD to get a true PHI spiral would be nice, I'm still looking into how to do this, my best lead is to use an algorithm or formula like you would to graph on say a calulator...


...the trick is how to do this in AutoCAD?  Maybe we could input it using some programming, may be tricky and I haven't found anything out there that was a true phi spiral only a fibonacci or other types of spirals.


The explanation to the 3D fibonacci squares, I simply added DEPTH to all the squares to in reality it creates another spiral in the Z-AXIS as well as a flat 2D plane.


I think JTStatic you are on to something with your comment about a line (1D) exists on the flat SQUARES (2D) environment.  I have been seeing the same phenomena with some pictures some may have seen a bit off topic here relating to dividing up a square.  I believe this is a phenomena of NATURE that it uses the PREVIOUS as a building block for the NEXT PIECE.  An example is simple...

... the FRACTIONS of the square have all the information to show the fractions to the next progression, (eg. 1/2 has all the info for 1/3, and 1/3 has all the info for 1/4, etc. to infinity)  I believe this is how nature works, very similar to how the FIBONACCI pattern is derived.  I'm sorry if this is off topic a bit, but as JTStatic pointed out the same applies to the spiral for DIMENSIONS, the 1D line on a 2D plane is connected, therefore we just need to see the information and it should already be in front of us to go further up.  Having said that, a 2D spiral might appear like a ROSE PETAL as a 2D object in a 3D world, so a 3D SPIRAL??? in a 4D plane, this could be for another topic, just thought I'd put it out there.

Here is another PHI picture that I love, notice how the DOUBLING SEQUENCE (124875) is incorporated here.  Again the PENTAGON the PHI-ve (5) is intersecting perfectly with the circle and the PHI ARC.




I'm interested in this one Riseball. Tell us some more about it if you would.... I cant see much in the image at that resolution. Where is the Phi ratio? and how did you get the arc etc.... I'm really interested in the connections between the doubling circuit and Phi....

Riseball said:

Here is another PHI picture that I love, notice how the DOUBLING SEQUENCE (124875) is incorporated here.  Again the PENTAGON the PHI-ve (5) is intersecting perfectly with the circle and the PHI ARC.




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