This is a modern reproduction of the first published image of the Mandelbrot set, which appeared in 1978 in a technical paper on
Kleinian groups by
Robert W. Brooks and Peter Matelski. The Mandelbrot set consists of the points c in the
complex plane that generate a bounded sequence of values when the recursive relation zn+1 = zn2 + c is repeatedly applied starting with z0 = 0. The boundary of the set is a highly complicated
fractal, revealing ever finer detail at increasing magnifications. The boundary also incorporates
smaller near-copies of the overall shape, a phenomenon known as quasi-
self-similarity. The
ASCII-art depiction seen in this image only hints at the complexity of the boundary of the set. Advances in computing power and computer graphics in the 1980s resulted in the publication of
high-resolution color images of the set (in which the colors of points outside the set reflect how quickly the corresponding sequences of complex numbers diverge), and made the Mandelbrot set widely known by the general public. Named by mathematicians
Adrien Douady and
John H. Hubbard in honor of
Benoit Mandelbrot, one of the first mathematicians to study the set in detail, the Mandelbrot set is closely related to the
Julia set, which was studied by
Gaston Julia beginning in the 1910s.
This is a modern reproduction of the first published image of the Mandelbrot set, which appeared in 1978 in a technical paper on
Kleinian groups by
Robert W. Brooks and Peter Matelski. The Mandelbrot set consists of the points c in the
complex plane that generate a bounded sequence of values when the recursive relation zn+1 = zn2 + c is repeatedly applied starting with z0 = 0. The boundary of the set is a highly complicated
fractal, revealing ever finer detail at increasing magnifications. The boundary also incorporates
smaller near-copies of the overall shape, a phenomenon known as quasi-
self-similarity. The
ASCII-art depiction seen in this image only hints at the complexity of the boundary of the set. Advances in computing power and computer graphics in the 1980s resulted in the publication of
high-resolution color images of the set (in which the colors of points outside the set reflect how quickly the corresponding sequences of complex numbers diverge), and made the Mandelbrot set widely known by the general public. Named by mathematicians
Adrien Douady and
John H. Hubbard in honor of
Benoit Mandelbrot, one of the first mathematicians to study the set in detail, the Mandelbrot set is closely related to the
Julia set, which was studied by
Gaston Julia beginning in the 1910s.