Fractals Freak Me Out
The Yiddish word mandelbrot literally means almond bread, a reference to its common ingredient of almonds. It is typically formed by baking a loaf which is then cut into small slabs and twice-baked in order to form a crunchy exterior. sort of like biscotti.
This has absolutely nothing to do with fractals; I just thought I’d toss it in for randomness, like croutons on a Caesar salad.
Fractals freak me out but they’re also super cool and I decided to learn a little bit about them since I’m immobile for a couple of days, recovering from a bad reaction to a pneumonia vaccination.
According to Wiki, Benoit B. Mandelbrot (20 November 1924–14 October 2010) was a Polish-born French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as “the art of roughness” of physical phenomena and “the uncontrolled element in life”.
He referred to himself as a “fractalist” and is recognized for his contribution to the field of fractal geometry, also coining the word “fractal”, as well as developing a theory of “roughness and self-similarity” in nature.
Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale’s history to receive tenure.
Fractals are also found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry:
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. (Mandelbrot, in his introduction to The Fractal Geometry of Nature)
Did you know there’s a Fractal Foundation? https://fractalfoundation.org/
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems — the pictures of Chaos. Or in my opinion, of heart-centered LOVE, an infinite woven pattern of infinity. Not finite. Not at all.
A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.
The most famous fractal equation is the 2D Mandelbrot set, named after Mandelbrot in 1975.
What is Mandelbrot set zoom?
It’s an image made purely of mathematics. It is formed by converting the coordinates of each pixel into a complex number and then iterating it with a simple equation. We can actually zoom into the picture by narrowing the range of the axes and get a better look at the detail along the edge of the set.
The spirals of florets on a Romanesco broccoli form natural fractals.
As it turns out, a lot of plant life grows in patterns that mimic the Fibonacci sequence with petals, leaves, or (in the case of Romanesco broccoli) tiny buds called “meristems” that have 1,2,3,5,8,21 and more spirals coming from the center.
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