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Symmetry in Chaos

paulbourke.net

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Re: Symmetry in Chaos

#31

Post by alimw »

abetusk wrote: post #20

These are awesome, but it would be nice to understand, even at some heuristic level, why they're periodic with the period they do have. Alternatively, what is a change to a completely periodic orbit to chaos with the same "periodic symmetry" that gives some enlightenment of where the chaos is being inserted and why it isn't destroying the periodic orbit. Does anyone have an idea of whats' going on, or references that…

All of these are aperiodic; it says as much in the first paragraph. Are you talking about the rotational symmetry?

Re: Symmetry in Chaos

#32

Post by pluijzer »

sandman1906 wrote: post #26
jes wrote: post #15

This reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.

Do you remember the title of it?

Web of Life

Here is the youtube video and transcript. I think the parent poster refered to section IV, around 19:20 in the video.

https://www.organism.earth/library/document/out-of-your-mind...

Re: Symmetry in Chaos

#33

Post by andybak »

passion__desire wrote: post #23
jes wrote: post #15

This reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.

To add some spice to your observation. I read somewhere that "This statement is false" can act as a oscillator, a "clock" going tick-tock, at the deepest level of reality.

Ok. I need to know more.

Re: Symmetry in Chaos

#34

Post by andybak »

jes wrote: post #15

This reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.

On the theme of "Unexpected Alan Watts" I'd like to recommend the game "Everything" which after a slightly bizarre start develops into a "achieve subgoal, get an Alan Watts audio clip as a reward" gameplay loop. It's fantastic.

Re: Symmetry in Chaos

#35

Post by jes »

andybak wrote: post #34
jes wrote: post #15

This reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.

On the theme of "Unexpected Alan Watts" I'd like to recommend the game "Everything" which after a slightly bizarre start develops into a "achieve subgoal, get an Alan Watts audio clip as a reward" gameplay loop. It's fantastic.

Will check it out! Ty!

Re: Symmetry in Chaos

#36

Post by jes »

passion__desire wrote: post #23
jes wrote: post #15

This reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.

To add some spice to your observation. I read somewhere that "This statement is false" can act as a oscillator, a "clock" going tick-tock, at the deepest level of reality.

Please say more!

Re: Symmetry in Chaos

#37

Post by jes »

pluijzer wrote: post #32
sandman1906 wrote: post #26

Earlier quoted context omitted.

Do you remember the title of it?

Web of Life Here is the youtube video and transcript. I think the parent poster refered to section IV, around 19:20 in the video. https://www.organism.earth/library/document/out-of-your-mind...

Perfect. Appreciate the ref.

Re: Symmetry in Chaos

#38

Post by cossatot »

Does anyone know where to find some code examples in which RGB images are generated from the equations? I don't really understand how the mathematical solution is translated into a raster/pixel image and what the colors correspond to. But I would love to start making playing with these.

Re: Symmetry in Chaos

#39

Post by IAmGraydon »

cossatot wrote: post #38

Does anyone know where to find some code examples in which RGB images are generated from the equations? I don't really understand how the mathematical solution is translated into a raster/pixel image and what the colors correspond to. But I would love to start making playing with these.

It's right there in the article:

> The images here are generated by iterating the series typically 1,000 million times. This is performed in two passes, the first pass with many fewer iterations is used to find the bounds of the attractor on the complex plane, the second pass actually "draws" the attractor points. The process of drawing involves treating the bounded region of the complex plane as a 2D histogram, each time the series passes through a pixel region on the plane the histogram at that location is incremented. One might imagine the 2D histogram as a height field, a larger values at a point indicate that the complex series passed through that pixel more often than a point with a smaller value. At the end of the process the histogram is mapped onto colours depending on the histogram values, there are many ways to do this based on aesthetic grounds.

Re: Symmetry in Chaos

#40

Post by abetusk »

dmbche wrote: post #29
abetusk wrote: post #25

Earlier quoted context omitted.

Could you point to the chapter or page?

I have a hard time pointing you somewhere, I think you should start with the first chapter and see from there, it's a good primer.

I've skimmed Gleick's book before and my feeling is that it's a high level overview of the subject without much content in either explaining the underlying math, the motivation behind it or giving some deeper insight into the subject, at least at a level that I would consider valuable.

I'm probably being too pejorative, but these books (like GEB or the like) are something I consider "feel good" books that give the illusion of understanding rather than any real insight. They're great for motivating people to learn more and popularizing mathematics as something to be valued but I find them to be very bad for actual understanding. As a litmus test, can you name any prediction that people can make after reading the book? Are there any falsifiable experiments that people can run?

Contrast this with John Baez's post on roots of polynomials with integer roots [0]. Not only are there pretty pictures but there's an in depth explanation of what the structures are and how they show up (IFS, connectivity, etc.).

Something along the line of Baez's treatment of roots of polynomials with integer coefficients is what I was looking for on how these structures show up in these chaotic systems.

[0] https://math.ucr.edu/home/baez/roots/

EDIT: "GEB" not "GED"

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