CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Initial image of a Mandelbrot set zoom sequence with a continuously colored environment Mandelbrot animation based on a static number of iterations per pixel Mandelbrot set detail The Mandelbrot set is the set of complex numbers c for which the sequence ( c , c ² + c , ( c ²+ c )² + c , (( c ²+ c )²+ c )² + c , ((( c ²+ c )²+ c )²+ c )² + c , …) does not approach infinity. The set is closely related to Julia sets (which include similarly complex shapes) and is named after the mathematician Benoit Mandelbrot , who studied and popularized it. Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each numb...