The Mandelbrot set is the set of complex numbers c for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge when iterated from z = 0 {\displaystyle z=0} , i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)} , f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))} , etc., remains bounded in absolute value.The set is closely related to the idea of Julia sets, which produce similarly complex shapes. Its definition and name are due to Adrien Douady, in tribute to the mathematician Benoit Mandelbrot.[1]Mandelbrot set images may be created by sampling the complex numbers and determining, for each sample point c, whether the result of iterating the above function goes to infinity. Treating the real and imaginary parts of each number c as image coordinates, pixels may then be colored according to how rapidly the sequence diverges, with the color 0 (black) usually used for points where the sequence does not diverge.Images of the Mandelbrot set exhibit an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. 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-similarity applies to the entire set, and not just to its parts.The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization.
Have you ever wondered what stuff you are made of and how you relate to it all starring upward to a starry night sky?
I have. What I found is that what is around me, out there, is in me here:
This is your brain:
This is the Universe:
Of course, like many others, I have my own reality theory on how this all is linked together.
What matters more than the stories we tell ourselves is the core value learned from the story.
What is your story? Does it have a good ending, a empowered beginning?
Do you see yourself in the world around you?
It is my hope that as we continue to replicate the life around us, that we honor the life in us, too.
Fly on Divine Fractals, fly on.
namaste,
zs.
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