MangoTime

About Me

Began in March 2011

A wikichallenged novice, getting started in this alien arena  

Watch this space...well, perhaps not yet.

To Do

• Upload pictures
• Put a box aroung Tip of the Day
• New article - for WWG of Aust NSW

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 ${\displaystyle c}$  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 ${\displaystyle -0.75+0.1i}$ , at increasing levels of magnification.Image credit: Wolfgang Beyer

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