Template:POTD/2025-08-30

Picture of the day

• 
  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 $c$ for which the function $f_{c}(z)=z^{2}+c$ does not diverge to infinity when iterated starting at $z=0$. 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 $-0.75+0.1i$, at increasing levels of magnification.Image credit: Wolfgang Beyer