![]() 40.3 MB WMV | 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. Here are some still image frames from the video to give an idea what it looks like. Each thumbnail below links to a full-sized image.
Abraham de MoivreThis 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). |