z = z * z + c
It is named after Benoit Mandelbrot who first mapped it. Melinda Green discovered an alternate method of drawing the Mandelbrot set, where instead of selecting initial points on the real-complex plane one for each pixel, initial points are selected randomly from the image region. Then, each initial point is iterated using the standard Mandelbrot function in order to test whether it escapes or not. Only those that do exit are then re-iterated. The areas that remain are called "strange attractors", the hidden islands of stability that emerge from a chaotic system, but are not simply random, they appear to reveal a deeper pattern and structure. The resulting image from such a function was called a "Buddhabrot", first named by Lori Gardi.
I find it hard to classify such a discovery as a mere coincidence! It must be true that simple formulas when reiterated infinitely over a seemingly infinite space (i.e. the universe) can only result in the current configuration we are experiencing today. How else could it be that an image from such a simple function result in an image that so much resembles the form that has emerged from millions of years of evolution of life on Earth, not to mention billions of years of cosmic evolution before that? The form I am speaking of, of course, is that of the human form.
Such natural functions of course do not always result in human forms. Variations on these functions result in other images of pure beauty that we experience just as much in the depths of outer space as we do on our own planet.
"At any given moment, life is completely senseless. But viewed over a period, it seems to reveal itself as an organism existing in time, having a purpose, trending in a certain direction." -Aldous Huxley
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