What is Fractal Zooming ?

The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoit Mandelbrot, who studied and popularized it.

Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.

More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial

z_{n+1}=z_n^2+c

remains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets.

The Mandelbrot set is self-similar under magnification in the neighborhoods of the Misiurewicz points. It is also conjectured to be self-similar around generalized Feigenbaum points (e.g., −1.401155 or −0.1528 + 1.0397i), in the sense of converging to a limit set.

Quasi-self-similarity in the Mandelbrot set

The Mandelbrot set in general is not strictly self-similar but it is quasi-self-similar, as small slightly different versions of itself can be found at arbitrarily small scales.

The little copies of the Mandelbrot set are all slightly different, mostly because of the thin threads connecting them to the main body of the set.



What did I do ?


I tried to apply the theory of Fractal Zooming, I tried it on a simpler scale to explain 
How we could look into ourselves in a simpler way ?

The experiment is as follows :

When you look inside your own eye in a mirror you normally see a black dot ! 

Where as 

When you look into another persons eye you see yourself.

Now the Manish Surprise 

In that person's eye when you see your face, look at your eye and try observing what you see in your own eye in that person's eye, multiply the effect and you observe that we get into a closed loop, What do you observe by doing this is still unknown, The most exciting part is when you try this experiment on animals ....

Fractal zooming quotes


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