truefract

Displays the boundaries of Mandelbrot and Julia sets on a pixelated digital display accurately by guaranteeing correctness using interval arithmetic.

The traditional method to draw fractals on a computer screen is to first choose an iteration limit. Then, for each pixel we compute the complex iteration of the associated fractal at a point corresponding to the center of the pixel enough number of times to determine the nature of the complex sequence produced at that point, but whose length is upper bounded by the iteration limit. While this is a compromise between accuracy and time for practical purposes, it does not make clear what the iteration limit must be to produce the "correct" fractal boundary on a pixelated display, where correctness is as defined below.

The problem of drawing a fractal boundary on a pixelated display is the problem of determining the pixels through which the fractal boundary passes and coloring only those pixels black. A drawing of this type is "correct" (this is as precise as the display would allow us to be).