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The quest to decode the Mandelbrot set

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Re: The quest to decode the Mandelbrot set

#31

Post by hnfong »

ggambetta wrote: post #19
hnfong wrote: post #12

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…

> 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. Honest question: what else do you think it could be, if not a coincidence?

Honest answer: some early Buddhist followers taking some form of acid/mushrooms and saw geometric visions of the Mandelbrot set and thought it was a divine manifestation of Buddha?

I mean, I don't think this is likely, but that's the best I got.

I hear the brain likes to go into geometry mode when hallucinogens are ingested, and I suppose the brain is theoretically powerful enough to compute the Mandelbrot sets...

Re: The quest to decode the Mandelbrot set

#32

Post by derbOac »

Does anyone know of any good resources on Kolmogorov complexity and fractals such as the Mandelbrot set? Or even on information theory and fractals?

For some reason reading this article is making me wonder about the difference between the information required to generate something like a mandelbrot, knowing the underlying rule, and the information required to represent it as it is, without following the rule. Or e.g., the difference between the information of the generating rule and the information implicitly represented through the time or number of operations needed to generate it.

It seems like there's some analogy between potential and kinetic energy, and kolmogorov complexity and something else, that I'm having trouble putting my finger on. Even if you have a simple generating algorithm that might be small in a kolmogorov complexity sense, if that algorithm entails a repeating something over a large number of operations, the resulting object would be complex, so there's an implied total complexity as well as an "generating" one.

Maybe this is some basic computational complexity concept but if so I'm not recalling this, or am being dense. E.g., I'm used to discussions of "compressibility" but not of the "generating representation information cost" versus "execution cost".

Re: The quest to decode the Mandelbrot set

#33

Post by armchairdweller »

hnfong wrote: post #31
ggambetta wrote: post #19

Earlier quoted context omitted.

> 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. Honest question: what else do you think it could be, if not a coincidence?

Honest answer: some early Buddhist followers taking some form of acid/mushrooms and saw geometric visions of the Mandelbrot set and thought it was a divine manifestation of Buddha? I mean, I don't think this is likely, but that's the best I got. I hear the brain likes to go into geometry mode when hallucinogens are ingested, and I suppose the brain is theoretically powerful enough to compute the Mandelbrot sets...

I have had similar thoughts.

The prominent modes and paths of this 2D probability distribution also show some resemblance to the kabbalistic tree of life, which is its own, but fairly related topic of study. DMT use within a connected strand of this "inner science" has been suspected.

Drawing more of these far-fetching connections: The complex plane is related to several areas of physics, which might somehow find expression in electromagnetic brain dynamics.

In any case, the buddhabrot distribution seems quite understudied both from a scientific / mathematical PoV, and from the perspectives of the occluded study of the "inner realms".

Re: The quest to decode the Mandelbrot set

#34

Post by crazygringo »

infogulch wrote: post #8

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/

I made quite a sophisticated viewer as a teen, but boy was it slow to run back then, back on a 486.

Now people write viewers that run lighting fast in a browser thanks to WebGPU! Like:

https://www.reddit.com/r/fractals/comments/o7l4bm/please_try...

Re: The quest to decode the Mandelbrot set

#35

Post by dcow »

derbOac wrote: post #32

Does anyone know of any good resources on Kolmogorov complexity and fractals such as the Mandelbrot set? Or even on information theory and fractals? For some reason reading this article is making me wonder about the difference between the information required to generate something like a mandelbrot, knowing the underlying rule, and the information required to represent it as it is, without following the rule. Or e.g.…

I think you’re forgetting that there’s no definitive way to represent something, compressed or raw. So while it’s interesting to acknowledge that we can compress data and sometimes rather efficiently, I’m not sure it maps to anything physical beyond the fact that decompressing data creates entropy.

Perhaps you’d be interested in https://en.wikipedia.org/wiki/Landauer%27s_principle. Turns out there may be a minimum energy required to decrease entropy. Jade has a really good overview https://youtu.be/XY-mbr-aAZE?si=7DvSs2DMudsh6gk8

Re: The quest to decode the Mandelbrot set

#36

Post by bongodongobob »

OscarCunningham wrote: post #29

What is the conjectured topology of the Mandelbrot set if MLC is true? My understanding is that there's a certain number of bulbs, each centred around a point which becomes periodic with period p after k steps. But how do they all stick together?

The entire set is connected iirc.

Re: The quest to decode the Mandelbrot set

#37

Post by IronBacon »

crazygringo wrote: post #34
infogulch wrote: post #8

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/

I made quite a sophisticated viewer as a teen, but boy was it slow to run back then, back on a 486. Now people write viewers that run lighting fast in a browser thanks to WebGPU! Like: https://www.reddit.com/r/fractals/comments/o7l4bm/please_try...

I remember as a teen I did mine in 68000 assembly on a Commodore Amiga to get it reasonable fast considering it was running on a 16 MHz CPU — i would say a few seconds to draw the canonical image — but IIRC it reached pretty fast the limit of math precision.

At that time I didn't know what was a complex number, but was fascinated by the whole concept of fractals and how complex structures could be created with a relative simple program.

Re: The quest to decode the Mandelbrot set

#38

Post by clintonc »

OscarCunningham wrote: post #29

What is the conjectured topology of the Mandelbrot set if MLC is true? My understanding is that there's a certain number of bulbs, each centred around a point which becomes periodic with period p after k steps. But how do they all stick together?

MLC stands for "Mandelbrot Locally Connected". It's not obvious, but this is equivalent to the bulbs of the Mandelbrot set (the domains of parameters where almost all points get attracted toward periodic orbits) are dense in the Mandelbrot set. Everyone believes it to be true.

Re: The quest to decode the Mandelbrot set

#39

Post by qazxcvbnm »

bongodongobob wrote: post #36
OscarCunningham wrote: post #29

What is the conjectured topology of the Mandelbrot set if MLC is true? My understanding is that there's a certain number of bulbs, each centred around a point which becomes periodic with period p after k steps. But how do they all stick together?

The entire set is connected iirc.

But what would be its homology, for instance?
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