Wikipedia picture of the day for August 30

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  • Initial image of the Mandelbrot set (1Γ— magnification)
    Initial image of the Mandelbrot set
    (1Γ— magnification)
  • Head and shoulder (6Γ— magnification)
    "Head and shoulder"
    (6Γ— magnification)
  • Seahorse valley (60Γ— magnification)
    "Seahorse valley"
    (60Γ— magnification)
  • Seahorse (191Γ— magnification)
    "Seahorse"
    (191Γ— magnification)
  • Seahorse tail (1345Γ— magnification)
    "Seahorse tail"
    (1345Γ— magnification)
  • Tail part (4169Γ— magnification)
    "Tail part"
    (4169Γ— magnification)

The Mandelbrot set is a two-dimensional mathematical set that is defined in the complex plane as the numbers
{\displaystyle c}
for which the function
{\displaystyle f_{c}(z)=z^{2}+c}
does not diverge to infinity when iterated starting at
{\displaystyle z=0}
. 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
{\displaystyle -0.75+0.1\mathrm {i} }
, at increasing levels of magnification.

Image credit: Wolfgang Beyer​


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