The Mandelbrot set is a two-dimensional set. It is defined in the complex plane as the complex numbers c for which the function f c = z 2 + c does not diverge to infinity when iterated starting at z =
The Mandelbrot set plotted on the complex plane within a continuously colored environment
Gap between the "head" and the "body", also called the "seahorse valley"
Double-spirals on the left, "seahorses" on the right
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals
Mandelbrot set
…and John H. Hubbard (1985), who established many of its fundamental properties and named the set in honor of Mandelbrot for his influential work in fractal geometry. The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books (1986), and an internationally…
Highly magnified area on the boundary of the Mandelbrot set
Mandelbrot set with 12 encirclements
2x 120 degrees recursive IFS