Fractals

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These two fractals were DRAWN BY HAND.
Fascinating story about it as well:

The man who hand-draws mathematical fractals - New APPS Art Politics Philosophy Science

One of the subjects I work with, JP, has acquired synesthesia and acquired savant syndrome. This happened as a result of a brutal assault in 2002, during which he was kicked and hit on the head. He was subsequently diagnosed with a bleeding kidney and an unspecified head injury. What the doctors didn't know was that JP no longer saw the world the way he used to. Objects suddenly did not have smooth boundaries. Things no longer moved smoothly. Motion took place in picture frames. It looked like someone paused and unpaused the flow of the world very rapidly. Even more amazing: JP was suddenly able to see vivid fractal images of objects with a fractal structure (such as, broccoli).

JP's response to his new way of seeing the world was to withdraw from it. He spent the following three years in his apartment and refused to leave unless it was strictly necessary. After three years in complete isolation JP figured that he would try to draw what he saw, so he could make people understand him. He started drawing. And he continued. He drew and drew and drew, using only a pencil, a ruler and a compass. The results were beautiful hand-drawn fractal-like images. JP didn't know then that he was the first in the world to hand-draw mathematical fractals and that he would later win prizes for his drawings. He didn't even know what he was drawing, except that it was what he saw.

A year later a mathematician came into the store where JP worked as a sales person. He saw some of JP's drawings and urged JP to take some college math courses. JP had barely passed his high school math exams. But he went back to school and learned a few basics that enabled him to describe to people in mathematical terms what he saw. Once he learned some basic equations for the structures he saw, these equations, too, would trigger fractal images.

 

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