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Maybe Mandelbrot shape represents a state space or set of possible transformations, configurations or relationships of certain solvable or equilibrium dynamical systems, so maybe MLC is true if there's a certain structure-preserving relationship over sets of these dynamical systems.
Yet something I learned recently blew my mind. It's about the uncanny resemblance between the images generated by the Mandelbrot set, and among all things, the popular image of Buddha.
For example: https://en.wikipedia.org/wiki/Buddhabrot
Even when looking at the 2D Mandelbrot set renderings, I can't help but wonder whether the similarity of the "bulbs" to the rather unique Buddha "hairstyle" (of allegedly funny lumps of hair) was just a coincidence.
Also, the tower-like makuṭa headdress in some Buddhist traditions look exactly like the thin threads that connect the bulbs at around (-2, 0).
I'm not saying they mean anything, but just something uncanny, and once I learned about the resemblance, it's hard to unsee it...
The Mandelbrot set is quite well known. Yet something I learned recently blew my mind. It's about the uncanny resemblance between the images generated by the Mandelbrot set, and among all things, the popular image of Buddha. For example: https://en.wikipedia.org/wiki/Buddhabrot Even when looking at the 2D Mandelbrot set renderings, I can't help but wonder whether the similarity of the "bulbs" to the rather unique Bud…
https://abcnews.go.com/Technology/WhosCounting/story?id=9861...
> the word evoked the notion of a new kind of geometry — something fragmented, fractional or broken. But that's not what "fractal" means; it means "fractional dimension". To say the word "fractal" evoked something is subjective - evoked it for whom?
Compare to the etymology section here
Making a program to render a view of the Mandelbrot set is a fun exercise, I recommend it. I found a viewer that works in the browser: > Mandelbrot Viewer is a universal (desktop and mobile) vanilla JS implementation of a plain Mandelbrot set renderer – supporting mouse, touch and keyboard interaction. https://mandelbrot.silversky.dev/
Here's my attempt done a long time ago, not very polished: https://brazzy.de/en/Mandelbrot.php Even for that, the actual Mandelbrot calculations were the smaller part. It's really amazing how such a trivially simple formula spawns such endless complexity.
Making a program to render a view of the Mandelbrot set is a fun exercise, I recommend it. I found a viewer that works in the browser: > Mandelbrot Viewer is a universal (desktop and mobile) vanilla JS implementation of a plain Mandelbrot set renderer – supporting mouse, touch and keyboard interaction. https://mandelbrot.silversky.dev/
... It's all elephants. The -R spike at the main disc is period 2, the fork around +/-i is period 3, and so on to infinity at 0.25+0i.
MLC might just be one of those facts that is true but unprovable!
The Mandelbrot set is quite well known. Yet something I learned recently blew my mind. It's about the uncanny resemblance between the images generated by the Mandelbrot set, and among all things, the popular image of Buddha. For example: https://en.wikipedia.org/wiki/Buddhabrot Even when looking at the 2D Mandelbrot set renderings, I can't help but wonder whether the similarity of the "bulbs" to the rather unique Bud…
Honest question: what else do you think it could be, if not a coincidence?
https://en.wikipedia.org/wiki/Buddhabrot
It is the probability distribution (i.e. the most frequent locations visited) over the trajectory of the points that escape the plane.
