About the Illustrations

David Beale

The animations are done by Microsoft's free gif animator). I use Dassault's DraftSight for most 2D illustrations if they can be done in only 2D otherwise Dassault's SolidWorks Premium does 3D and 2D pictures such as the gold background image of tangential circles within circles (a type of fractal). The dwg package outputs SVGs, into Corel PaintShop Pro Ultimate x8 to get gifs, Irfanview batch to trim and make transparent. 256 colours make smooth transitions but I like 16 colours, for gifs, because the transitions cause movement effects which help remind about the idea that all oscillating force-field bits have the harmonics of the whole of Creation, to some infinitessimal amount above zero, with other harmonics enabling each particle, no matter how simple, to be unique in ways additional to no two particles being able to fully occupy the same place in space at the same time.

The table below is used for the spherical moving diagrams. I compared matching the diameters to the sine of the angle (0, 7.5, 15...) to squaring (after multiplying the sine value to make useable diameter sizes). I wanted to illustrate the idea of sharing multi-dimensional space concentrically and equally so as to form stable occupancy; and as one diminishes the other increases with the total (100% occupancy) remaining constant in all dimensions; so sine-squared times 10 is better than without first squaring sine. Also the latter shows a slightly more obvious change in size from 90degrees to 82.5. I believe the analog is better for squaring the diameter (sine) first; because the exclusion forces are proportional to 2D not the gravity quantity (cubic). The exclusion force has to work in all directions, so the inverse-square rule works. An earlier animation, purple, has two bits of force-field sharing 3D space and phased compatible enough to be forced together tangentially but not concentrically. The bits go away and come back, in 3D; between them occupying space with enough stability for the pair to be a part of larger patterns.

degrees | sine x 100 0 to 90 | sin x 100 90 to 0 | degrees | sum B+C | sin-sqx10 zero to 90deg | 90 to 0 | 100 |

0.0 | 0.000 | 100.000 | 90.0 | 100.000 | 0.000 | 100.000 | 100.000 |

7.5 | 13.053 | 99.144 | 82.5 | 112.197 | 1.704 | 98.296 | 100.000 |

15.0 | 25.882 | 96.593 | 75.0 | 122.474 | 6.699 | 93.301 | 100.000 |

22.5 | 38.268 | 92.388 | 67.5 | 130.656 | 14.645 | 85.355 | 100.000 |

30.0 | 50.000 | 86.603 | 60.0 | 136.603 | 25.000 | 75.000 | 100.000 |

37.5 | 60.876 | 79.335 | 52.5 | 140.211 | 37.059 | 62.941 | 100.000 |

45.0 | 70.711 | 70.711 | 45.0 | 141.421 | 50.000 | 50.000 | 100.000 |

52.5 | 79.335 | 60.876 | 37.5 | 140.211 | 62.941 | 37.059 | 100.000 |

60.0 | 86.603 | 50.000 | 30.0 | 136.603 | 75.000 | 25.000 | 100.000 |

67.5 | 92.388 | 38.268 | 22.5 | 130.656 | 85.355 | 14.645 | 100.000 |

75.0 | 96.593 | 25.882 | 15.0 | 122.474 | 93.301 | 6.699 | 100.000 |

82.5 | 99.144 | 9.000 | 7.5 | 108.144 | 98.296 | 1.704 | 100.000 |

90.0 | 100.000 | 0.000 | 0.0 | 100.000 | 100.000 | 0.000 | 100.000 |

=100*(SIN(RADIANS(An))) | =(10*(SIN(RADIANS(An))))^2 |