## Vortex math alternative mapping

October 4, 2018

## Square root 2 tuning of number collapse harmonics

August 24, 2018

## 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!

Above: x8 magnification

Above: x256 magnification

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 |

Above: visualization of Inverse wave pattern

Below: visualization of standard wave pattern