maria on fractal ness
maria popova on fractal thinking ness
via tweet [https://x.com/themarginalian/status/1841692907763315144]:
“In the mind’s eye, a fractal is a way of seeing infinity.”
The pattern inside the pattern – fractals, the hidden order beneath chaos, and the story of the refugee who revolutionized the mathematics of reality
and post [https://www.themarginalian.org/2021/02/22/mandelbrot-fractals-chaos/]:
The Pattern Inside the Pattern: Fractals, the Hidden Order Beneath Chaos, and the Story of the Refugee Who Revolutionized the Mathematics of Reality
A self-described “nomad-by-choice” and “pioneer-by-necessity,” Mandelbrot believed that “the rare scholars who are nomads-by–choice are essential to the intellectual welfare of the settled disciplines.” He lived the proof with his discovery of a patterned order underlying a great many apparent irregularities in nature — a sweeping symmetry of nested self-similarities repeated recursively in what may at first read as chaos.
gleick: He was the one who let us appreciate chaos in all its glory, the noisy, the wayward and the freakish, from the very small to the very large.. Over and over again, the world displays a regular irregularity.. In the mind’s eye, a fractal is a way of seeing infinity.
In all, his schooling was irregular and discontinuous. He claimed never to have learned the alphabet or, more significantly, multiplication tables past the fives. Still, he had a gift.
In physics and chemistry, where he could not apply geometry, he got poor grades. But in mathematics, questions he could never have answered using proper techniques melted away in the face of his manipulations of shapes.
At the heart of Mandelbrot’s mathematical revolution, this exquisite plaything of the mind, is the idea of self-similarity — a fractal curve looks exactly the same as you zoom all the way out and all the way in, across all available scales of magnification. Gleick describes the nested recursion of self-similarity as “symmetry across scale,” “pattern inside of a pattern.”
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be you. 