Sergey Khashin

Fast Mandelbrot set with infinite resolution, ver. 2

(Mandelbrot images with an extremely high magnification)

ver. 1 (Jointly with my Master student Kruchenkova T.)

A significant number of people in the world has been devoting a significant amount of time to the implementation of the Mandelbrot set. The main problem is that double precision gets exhausted very fast, while the arbitrary presion realizations are terribly slow. Below we demostrate our java implementation which works rather fast and with arbitrary precision.

For comparision:

Sergey Khashin Fast Mandelbrot set with infinite resolution (this page), July 9, 2011
On a standard home PC java computes a single picture with arbitary high resolution for some seconds. My program computes similar or the same series of pictures to those computed by others scientists about 1000 times faster! Proper benchmarking will appear hopefully soon. This significant accelation is obtained due to purely mathematical improvements of the existing algorithms.

Orson Wang Fractal Journey , April 30, 2011
A visual exploration of fractal geometry, Outtake: Mandelbrot Ultra Zoom. "All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months"

David Madore Mandelbrot set images and videos My program uses the GMP library for arbitrary precision floats. "I distributed computation on a pool of 30ish dual-core PC's, which ran for about one night to produce these videos."

A brief mathematical description

Click on some place of the picture to get a doubling of its scale with the center at the selected point.
The number printed above the image indicates the current square size in the complex plane.

Нажав мышкой в некоторое место картинки, мы получим удвоение ее масштаба с центром в выбранной точке.
Число над изображением означает текущий размер квадрата на комплексной плоскости.

For beginners: it is more interesting to click on the border of black region.

You need to install Java plugin for the browser to execute Java-applets.
For Ubuntu 11.04: install Icedtea plugin via Sinaptic

800 size

Sergey Khashin	Fast Mandelbrot set with infinite resolution (this page), July 9, 2011	On a standard home PC java computes a single picture with arbitary high resolution for some seconds. My program computes similar or the same series of pictures to those computed by others scientists about 1000 times faster! Proper benchmarking will appear hopefully soon. This significant accelation is obtained due to purely mathematical improvements of the existing algorithms.
Orson Wang	Fractal Journey , April 30, 2011 A visual exploration of fractal geometry, Outtake: Mandelbrot Ultra Zoom.	"All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months"
David Madore	Mandelbrot set images and videos My program uses the GMP library for arbitrary precision floats.	"I distributed computation on a pool of 30ish dual-core PC's, which ran for about one night to produce these videos."