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High-Precision Deep Zoom

Animations

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.

Sample Snapshots
UUE1-InitialFrameUUE1-Clip1UUE1-Clip2UUE1-Clip3UUE1-Clip4
UUE1-Clip5UUE1-Clip6UUE1-Clip7UUE1-FinalFrame
Download Options
MP4320x240 768 kbps 18.5 MB quick download quality
640x480 4Mbps 87.1 MB extreme quality
WMV320x480 768 kbps 21.1 MB quick download quality
Vital Statistics
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 = (1+√5).