Emergent spiral galaxy patterns

August 17, 2018

Above: output from wave harmonics visualizer with new 'Squared galaxy' algorithm with some color enhancements. A rendering bug causes the dark spot in the center, although in terms of making something pretty, I don't mind it!

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Above: x8 magnification

Above: x256 magnification

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Above: x8 magnification

Above: x64 magnification

'Concentric orthogonal field progressions' in the 'Root square' and connection to angles within regular Polyhedron

August 4, 2018

Below is the basic geometry structure I call the 'Root square'. Here it is arbitrary truncated at 32. Each parallel x and y line is plotted at square-root(n)

Some interesting results. I suspect there are a bunch more angles found in Platonic solids hiding in these square root progressions.

Below: A cursory observation connecting progressions above for different value n to the Dihedral angle of the regular Polyhedron

Polyhedron Dihedral angle f(n)
Tetrahedron 70.53° 90 - f(8) = 70.53
Cube 90°
Octahedron 109.47° 90 + f(8) = 109.47
Dodecahedron 116.57° 90 + f(4) = 116.57
Icosahedron 138.189685° ?
4-simplex 75.5225° f(15) = 75.5225
Hypercube 90°
Cross-polytope 120°
24-cell 120°
120-cell 144°
600-cell 164.478° 240 - f(15) = 164.478

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Above: visualization of Inverse wave pattern

Below: visualization of standard wave pattern

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