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Initial image of the Mandelbrot set (1× magnification)
"Head and shoulder" (6× magnification)
"Seahorse valley" (60× magnification)
"Seahorse" (191× magnification)
"Seahorse tail" (1345× magnification)
"Tail part" (4169× magnification)
The Mandelbrot set is a two-dimensional mathematical set that is defined in the complex plane as the numbers for which the function does not diverge to infinity when iterated starting at . It was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups, with Benoit Mandelbrot obtaining the first high-quality visualizations of the set two years later. Images of the Mandelbrot set exhibit an infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve. The Mandelbrot set is well-known outside mathematics and is commonly cited as an example of mathematical beauty. These images, generated by a computer program, show an area of the Mandelbrot set known as "seahorse valley", which is centred on the point , at increasing levels of magnification.
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