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High-Precision Deep Zoom
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Ununennius (UUE1) "de Moivre"
The deepest Mandelbrot set zoom ever?
This is, to date, the deepest no-nonsense, full-resolution, full-speed animation ever created that hpdz.net is aware of. It zooms to a final size of 9e-120, which is equivalent to a FractInt magnification of 2.2e119.
By no-nonsense I mean it is not done with any kind of frame interpolation or "tweening" of frames, but rather each frame is individually calculated individually. Full-resolution means each frame is 640x480, and full-speed means there are 30 raw data frames per second.
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| MP4 | 320x240 768 kbps 18.5 MB quick download quality 640x480 4Mbps 87.1 MB extreme quality |
| WMV | 320x480 768 kbps 21.1 MB quick download quality |
| Date Generated: | 11 Jun - 27 Jun 2008 |
| Final Image Size: | 9e-120 |
| Resolution: | 640x480 |
| Video Length: | 4:00 of fractal, 4:56 total |
| Frames: | 7200 |
| Rendering Time: | 120:40 hours |
| Method: | Escape counts |
| Audio: | Custom using Acid Pro 6 |
Abraham de Moivre
This video is also named in honor of Abraham de Moivre (1667-1754). De Moivre was a French mathematician most famous for his discovery of the relation in complex arithmetic that bears his name:
(cos a + i sin a)n = cos na + i sin na
Errata: The closely-related formula below, which I previously had shown as De Moivre's formula, is actually Euler's formula:
cos a + i sin a = e ia
De Moivre also worked in probability theory and number theory, and was the first to discover the closed-form expression for the Fibonacci numbers that for some reason today is known as Binet's formula:
F(n) = [φn - (-φ)-n]/√5
where φ is the Golden Ratio, φ = ½(1+√5).
All content Copyright by Michael Condron. All rights reserved unless otherwise noted.
You may download, save, and print a single copy for personal use only.
Music by various sources used with permission.
Please refer to individual video file credits for details.
