
where f is a Mandelbrot lemniscate The Mandelbrot set
is one of the most popular fractals, on many places on the
internet pictures (often colored) of the curve are to be seen. Before Mandelbrot already the Hungarian mathematician Riesz (1952) posed
questions related tot the Mandelbrot set. In 1978 Brooks and Matelski
made the first computer graphics of the curve. Adrien Douady and John Hubbard
studied the curve, they proved that the set is connected, and named it to
Mandelbrot. The main part of the curve, on the right, has the form of a cardioid; the part on the right has the form of a circle. 