Mathematics · Study 041
Mandelbrot Dive
An interactive Mandelbrot set that renders line by line and zooms wherever you click, down to the limits of floating point precision.
What you're looking at
For each pixel, a complex number c is fed into the rule z becomes z squared plus c, starting from zero. If z stays bounded forever, the pixel is inside the set and painted black. Otherwise its colour records how quickly z escaped. The image is drawn eighteen rows per frame so you can watch the computation sweep down.
The idea behind it
Benoit Mandelbrot plotted the set at IBM in 1980. Its boundary is infinitely detailed, and tiny distorted copies of the whole shape sit along every filament. Left alone, this study dives toward a well known spot in the region called Seahorse Valley.
Try this
Click or tap any point to zoom in three times, centred there. Leave it alone and it dives on its own.
