## Emergent spiral galaxy patterns

Aug 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

## Self simliar Moire patterns in square root concentric progression

Aug 6, 2018

Move Scale slider above to see concentric moiré patterns that seem to echo the parent progression of alternating black and white circles of sqRt(n) radius. The browser anti-aliasing is turned off with css for these images to prevent the browser's own smoothing algorithms from blurring out the Moiré effect. These images do not get swapped out when scaling. We find any pattern formed with this progression produces self echoing concentric moiré patterns. The effect is much more pronounced viewing in Firefox due to different rendering algorithms I assume.

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

Aug 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 |