Mandelbrot

[Yomama20]

The Mandelbrot set is the set of complex numbers  for which the function  does not diverge when iterated from , i.e., for which the sequence , , etc., remains bounded in absolute value.

The Mandelbrot set (black) within a continuously colored environment

Play media

Progressive infinite iterations of the "Nautilus" section of the Mandelbrot Set rendered using webGL

Mandelbrot animation based on a static number of iterations per pixel

Mandelbrot set detail

Zooming into the Mandelbrot set

Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot.^[1] The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes.

Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point , whether the sequence  goes to infinity (in practice – whether it leaves some predetermined bounded neighborhood of 0 after a predetermined number of iterations). Treating the real and imaginary parts of as image coordinates on the complex plane, pixels may then be coloured according to how soon the sequence  crosses an arbitrarily chosen threshold, with a special color (usually black) used for the values of  for which the sequence has not crossed the threshold after the predetermined number of iterations (this is necessary to clearly distinguish the Mandelbrot set image from the image of its complement). If  is held constant and the initial value of —denoted by —is variable instead, one obtains the corresponding Julia set for each point  in the parameter space of the simple function.

Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications. In other words, the boundary of the Mandelbrot set is a fractal curve. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarityapplies to the entire set, and not just to its parts.
 

cut copy pasted from wiki

[mirchi_bajji]

numberphile videos on youtuve show some interesting stuff in mathematics. 

amazing that mathematicians could do these without computers

[IdleBrain]

[johnydanylee]

@Catabolite @BeautyQueen @Catalpha @Ellen ravalammma

[Ellen]

9 hours ago, johnydanylee said:

@Catabolite @BeautyQueen @Catalpha @Ellen ravalammma

I did generative art based on these fractals by combining sinusoidal and cosine waves. It's great to play around with these equations ...you can use python turtle library to generate these functions 

[Nimmakai]

😳

[Yomama20]

4 hours ago, Ellen said:

I did generative art based on these fractals by combining sinusoidal and cosine waves. It's great to play around with these equations ...you can use python turtle library to generate these functions 

Okay 👍🏽