The quest to decode the Mandelbrot set
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The quest to decode the Mandelbrot set
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Re: The quest to decode the Mandelbrot set
#2If you enjoyed learning about the Hashlife algorithm for Conway's Game of Life, the bilinear approximation algorithm for computing whether a point is in the mandelbrot set has the same je ne sais quoi. No one has done a really accessible writeup of it yet, but this blog post and the linked forum thread are a good start: https://mathr.co.uk/blog/2022-02-21_deep_zoom_theory_and_pra...
Re: The quest to decode the Mandelbrot set
#3[deleted]
Re: The quest to decode the Mandelbrot set
#4Maybe 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.
Re: The quest to decode the Mandelbrot set
#5Decades ago two mathematicians argued about the area of the mandelbrot set. Both argued an asymtoically approaching different numbers. They started a distributed project to calculate the area.
I donated time on PA-risc workstations to the effort and was surprised to hear that the 2 machines contributed more to the final answer then 100s of other contributors. Something about how HP's compiler/chip preserved more accurate in the intermediate results than others. That surprised me since AFAIK the PA-risc is just a normal 64 bit floating point unit, which doesn't every have more precision for intermediate results. I believe PCs at the time often used the x86, which has 80 bits of precision for the intermediate results.
I believe the project was a success, but I don't remember the conclusion.
Re: The quest to decode the Mandelbrot set
#6Decades ago two mathematicians argued about the area of the mandelbrot set. Both argued an asymtoically approaching different numbers. They started a distributed project to calculate the area. I donated time on PA-risc workstations to the effort and was surprised to hear that the 2 machines contributed more to the final answer then 100s of other contributors. Something about how HP's compiler/chip preserved more accu…
More context here (alt.fractals discussion from February 1991) [0]:
[...] by computing the area of the M-set using lots of terms in a series (Laurent Series?), the upper bound of the area seems to converge about at 1.72 (the graph gets quite flat, and seems to have an asymptote there), and by counting pixals more and more accurately, you seem to get a lower bound of very close to 1.52. Both these bounds are close to the values the methods would produce in the limit - that is, it is NOT the case that these numbers would get closer if a finer grid were used, or more terms were taken in the series. So, why the difference of 10% or so? No one knows.
Re: The quest to decode the Mandelbrot set
#7> 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?
Re: The quest to decode the Mandelbrot set
#8Making 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.
Re: The quest to decode the Mandelbrot set
#9'“We’ve got to try to train a neural network to zoom around the Mandelbrot set,” Kapiamba joked.'
This actually sounds to me to be fine goal. An AI that sounds out unexplored depths to reveal interesting sights that maybe resemble what we see in the world at our level or cool patterns that potentially are a delight to the eye would be pretty cool.
Re: The quest to decode the Mandelbrot set
#10Making 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.