Octagonal Complexigram

[bdsign]

Q: ... (A) Okay, I was trying to figure out how to build this expanded gravity, and I made a table to assist the question. The first possibility is that one can build gravity on a square matrix. This matrix can be symmetric, can be non-symmetric, or can be a complex matrix, which I call possibilities a, b, and c. The second possibility is to build a theory of gravity on the basis of a connection which looks like a cube rather than a matrix. Here we also have three possibilities: no curvature, but torsion; no torsion but curvature; torsion and curvature. These are possibilities 1, 2, and 3. Another possibility is to use any combination of these two lines of speculation. Another possibility is none of the above, but to build gravity on the basis of an irregular cube, or an irregular square, which I call A. Another possibility is to use something that is none of the above.

A: Octagonal complexigram. Try the formula for possibility 1-c first.

Could this possibly be what the Cs call an Octagonal Complexigram?

And here are some other perspectives:

Sources:

Left:
Jadczyk A (2003) ‘On Quantum Iterated Function Systems’ IFT University of Wroclaw internal report
Blanchard P, Jadczyk A (1993) ‘Event Enhanced Quantum Theory and Piecewise Deterministic Dynamics’ Physical Letters A 175, pp. 157-164
Blanchard P, Jadczyk A, Ruschhaupt A (1999) ‘How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time’ e-print archive quant-ph/9911113
Gugg C, Healy T, Maier-Paape HK, Maier-Paape S[/b] (2000) ‘Nonlinear Standing and Rotating Waves on the Sphere’ Journal of Differential Equations 166, pp. 402-442

Middle:
Lipshitz R (2002) ‘The Square Fibonacci Tiling’ Journal of Alloys and Compounds 342, pp. 186-190

Right:
Cervenka M, Bednarik M and Konicek P (2003) ‘Nonlinear Standing Waves in Acoustic Resonators with Arbitrary Reflection Coefficients at Their Walls’ Czech Technical University, Prague

 

[ark]

I don't know. Complexigram suggests using complex numbers and complex spaces. That may relate to the formalism of quantum theory. But also to electromagnetism. Hard to say. In the mean time you may have fun watching my short 3D animation of a fractal related to "quantum octahedron". From outside and from inside.

http://www.youtube.com/watch?v=YNzf1o4GAAY

http://www.youtube.com/watch?v=HLHGpEk6Hsg

 

[bdsign]

Hi Ark,
Thanks for the links. Nice animations. I see your model is coming along nicely! It reminds me of resonance in bone formation or else I would guess resonant architecture of the future, on water! :)

I found some more fun things to meditate on. I thought these patterns were a nice visual to illustrate gravity waves based on the formula:

Zn+1 = Zn2

Paul Bourke's resonance patterns (below) were used to make the rendering of the big globe depicting gravity waves at the top of this thread based on your Octagonal Quantum Fractal (unfortunately, I don't have your original image that this globe was based on so I put the second smaller cross perspective [image above] in its place).

_http://paulbourke.net/fractals/circlesquares/index.html

Source:
Bourke P (1990) ‘Circle Squares Fractal’ University of Western Australia, online · http://local.wasp.uwa.edu.au/~pbourke/fractals/circlesquares/

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Here, you can clearly see Bourke's resonance patterns flashing negative/positive which are the exact same patterns as on the US Naval Research Laboratory's 'Pacific Radar Anomaly' Satellite data.

GOES-10 satellite data for the infrared spectrum from the night of December 7-8, 2001 (above and below)

Image enhancement of the GOES-10 data using the four-dimensional iterated function Zn+1 = Zn2

Source:
Steadman K (2002) ‘Pacific Radar Anomaly’ CyberspaceOrbit.com, online · http://www.cyberspaceorbit.com/pacific_anomaly.html

_____________________________

And more examples of this formula in nature:

Quantum fractal (left) describes calcite refraction (top right) and the structure of the electron (bottom right)

1973 Field Ion Micrograph of Platinum (left) Laser light casts the first atomic shadow ever photographed (right).

Source:
Image David Seidman (left) National Geographic News, Image Kielpinski Group, Griffith University. (right)

_____________________________


In case you want to play with some code:

The code for fractals, circles. squares:
_http://paulbourke.net/fractals/circlesquares/bmp.py

The code for fractals, circles. squares, thin lens:
_http://paulbourke.net/fractals/circlesquares/thin_lens.py

_____________________________

Lastly, I don't know if you saw these clips of physics papers on gravity waves I posted on another thread. I'll post them here too since they pertain to what I am showing here. I thought they would be helpful since gravity waves were mentioned in the past Cs session. http://cassiopaea.org/forum/index.php/topic,30965.0.html

 

[seiw83]

i may sugest that any patern close to flower of live is more adjustable. You can use any geometric form that you can inscribe into eart shape and find vertex. Your patern looks well. But all is simple. We perceive only multpication of simple forms.

 

[MoonGlow]

This is a pretty good visualization of what a square looks like blown out to a cube, a hypercube, and up to six dimensions:

http://www.youtube.com/watch?v=-x4P65EKjt0

Obviously, the concept can be applied to any geometric shape. It takes a ton of computer power, but there are also some three- and four-dimensional representations of the Mandlebrot set and its infinite complexity across higher dimensions.

If you're keen on the math involved, there's a joke in there:

Multiplication is repeated addition. Exponentation is repeated multiplication. The next hyper-operator is tetration, followed by pentration. The sixth hyper-operator is sexation. Why? Because sexation is repeated pentration.

True story.

 

[EmeraldHope]

This link is close enough for horse shoes for what I "see". _http://imgur.com/tYk1BBN


Mod's note: Link deactivated