High-Precision Deep Zoom


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
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
Video Length:4:00 of fractal, 4:56 total
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).