10 February 2010

Setul Mandelbrot zoomat de 10^214 ori

Tot filmul de mai jos e inclus in formula "z(n+1) = z(n)^2 + p", cu z si p numere complexe. Un punct p = (x,y) din grafic e negru daca recurenta plecand de la z(0) = 0 tinde la zero - adica z(infinit) = 0; un punct e colorat daca recurenta tinde la infinit, culoarea indicand cat de repede merge z spre infinit. Graficul obtinut nu are nici o continuitate, motiv pentru care oricat de mult e zoomat se obtin detalii suplimentare. Cu exceptia unor puncte speciale din grafic, procesul de zoomare nu aduce din nou si din nou aceeasi imagine, ci aduce imagini perpetuu diferite (chiar daca uneori seamana intre ele). Ceea ce e spectaculos e ca toata aceasta creativitate literalmente infinita se gaseste intr-o formula matematica atat de simpla.

Despre film:

The final magnification is 10^214. Want some perspective? A magnification of 10^12 would increase the size of a particle to the same as the Earth’s orbit! 10^21 would make a particle look the same size as the Milky Way and 10^42 would be equal to the universe. This zoom smashes all of them all away. If you were "actually" traveling into the fractal your speed would be faster than the speed of light.

You might like to know that this animation took me about two days to set up. My computer then rendered day and night non-stop for just over a month to produce the animation.

Mandelbrot Fractal Set Trip To e214 HD from teamfresh on Vimeo.