7 ms·
Symmetry in Chaos
- progrus 3y ago[flagged]
- ykonstant 3y agoThose are gorgeous; I would enjoy some explanation on how the authors came to investigate these particular recurrences.
- Horffupolde 3y agoI would argue that position-symmetry is not unexpected in a chaotic system. Symmetry means that one of your dimensions is redundant.
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- ironSkillet 3y agoWhy does it mean that?
- jfoutz 3y agoI'm not an expert, but think about linear algebra. you can write each dimension value in terms of time t(a) -> t(b) x = sin(t) y = 2cos(t) or whatever. if there is a symmetry, one of those equations should cancel out. another way to look at it is, if you can always get x, and know y "for free", or the other way around, then x and y aren't really independent. there's some other thing, like sqrt(t) that's generating both values.
- defrost 3y agoMarty Golubitsky's Homepage https://www.asc.ohio-state.edu/golubitsky.4/ https://www.asc.ohio-state.edu/golubitsky.4/ Books by same: https://www.asc.ohio-state.edu/golubitsky.4/mgbooks.html https://www.asc.ohio-state.edu/golubitsky.4/mgbooks.html https://en.wikipedia.org/wiki/Marty_Golubitsky https://en.wikipedia.org/wiki/Marty_Golubitsky Fearful Symmetry: Is God a Geometer? Ian Stewart + Martin Golubitsky is a good read, Ian Stewart is well known to UK recreational math fans and frequently hosts STEM material on th BBC. https://www.goodreads.com/en/book/show/1651085 https://www.goodreads.com/en/book/show/1651085 This sequel to the bestselling *Does God Play Dice?* will open your eyes to the broken symmetries that lie all around you, from the shapes of clouds to the drops of dew on a spider's web, from centipedes to corn circles. It will take you to the farthest reaches of the universe and bring you face-to-face with some of the deepest questions of modern physics.
- pixl97 3y agoWhat's interesting about physics is almost everything us symmetrical at the most fundamental levels. An interesting violation here is the charge parity symmetry, which may explain why matter exists in large quantities and anti matter does not. Symmetry violations like this may also explain why we have an arrow of time that runs in one direction.
- talkingtab 3y ago"A new kind of Science". Wolfram. Don't leave home without it. Seriously though. We talk about AI, but In My Opinion, the most powerful and interesting game changer is "Complex Adaptive Systems". I call them gestalts - the sum is greater than the parts because of how the parts interact to produce behaviors. Gestalts are all around us and we seem bizarrely unaware of them. Do you have some money? That means you are participating in a complex adaptive system or gestalt. Got cells? Perhaps you are a gestalt? Are you self aware? Does that mean you are a self aware gestalt, participating in other gestalts. Etc. The difficult question is whether you (yes you personally) can build a gestalt. Can you take some pieces - entities - give them a set of rules and get them to do some accomplish a purpose. That is the problem Wolfram was asking The RIP router is a defunct example that has all the pieces. Entities + Ability to interact + rules => function. Oh, and don't forget to vote.
- defrost 3y agohttp://bactra.org/reviews/wolfram/ http://bactra.org/reviews/wolfram/
- VHRanger 3y agoThanks, whenever Wolframs stuff comes up that bactra piece and this one: singlelunch.com/2020/04/23/why-stephen-wolframs-research-program-is-a-dead-end Should be mentioned since people should have the context that he's considered a crank byoat everyone in the communities he's doing research in
- fellowmartian 3y agoI used to believe in the “sum is greater than the parts” bit, in the context of emergence etc, but then I’d realized it’s at odds with basic information theory: where does the information go? what computes these behaviors? To me the answer is pretty clear: you’re outsourcing some of your storage and compute into the environment. Without a suitable substrate none of this would be possible.
- ilaksh 3y agoIn other words, metasystems via metasystem transitions. See Cosmic Evolutionary Philosophy and a Dialectical Approach to Technological Singularity https://www.semanticscholar.org/paper/Cosmic-Evolutionary-Philosophy-and-a-Dialectical-to-Last/d16d55bf034dd5580d3dc3759f94f9279c1e8c13 https://www.semanticscholar.org/paper/Cosmic-Evolutionary-Ph...
- euroderf 3y agoPlease stop feeding drugs to my pet Spirograph.
- deleted 3y ago[deleted]
- HDevo 3y agoPaul Bourke's website is great; don't forget to check his other articles! Over 10 years ago, it inspired me to play with strange attractors, which eventually ended with me writing https://github.com/chaoskit/chaoskit https://github.com/chaoskit/chaoskit. It was fun and I learned a lot, but it's definitely a deep rabbit hole. I've moved on since then.
- jes 3y agoThis reminds me of an Alan Watt's talk on alternating levels of order and chaos in nature.
- passion__desire 3y agoTo 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.
- andybak 3y agoOk. I need to know more.
- passion__desire 3y agoWell actually, it was a comment on a blogpost (I don't know what it was about). It said since if our world is a simulation, then it needs a computer to run on. And every computer needs a clock. So this statement changing its truth value could act as a clock.
- jes 3y agoPlease say more!
- sandman1906 3y agoDo you remember the title of it?
- pluijzer 3y agoWeb 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-3#ch4 https://www.organism.earth/library/document/out-of-your-mind...
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- abetusk 3y agoThese 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 I can look at?
- dmbche 3y agoJames Gleick's "Chaos: Making a new science" will answer your questions and is a fun read!
- abetusk 3y agoCould you point to the chapter or page?
- dmbche 3y agoI 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.
- abetusk 3y agoI'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/ https://math.ucr.edu/home/baez/roots/ EDIT: "GEB" not "GED"
- viesauvage 3y ago> Chaos I think there's more like a semantic slipping over this term, so that chaos ends up passing for another kind of order. Chaos is chaos. It's a bunch of really random stuff happening within an undefined, undetermined space, with randomly variable means. Like a landslide is chaos. The arrangement of stuff post-landslide will be a complete, incoherent, unpredictable mess. Today's normie "scientific" definition of "chaos" is what stands for "weird" or more accurately, ASYMMETRICAL. More philosophy, please.
- DonHopkins 3y agoNo, Chaos is the enemy of Control! https://www.youtube.com/watch?v=3KF5NfzmIvU https://www.youtube.com/watch?v=3KF5NfzmIvU "This is KAOS. We don't shoosh here!"
- DonHopkins 3y agoAlso check out Jim "Chaos" Crutchfield's work, and the mesmerizing video feedback he made with his analog video processing computer that he built at the University of California, Santa Cruz for his Ph.D. in physics in 1984. Jim Crutchfield https://en.wikipedia.org/wiki/James_P._Crutchfield https://en.wikipedia.org/wiki/James_P._Crutchfield https://csc.ucdavis.edu/~chaos/index.html https://csc.ucdavis.edu/~chaos/index.html Space-Time Dynamics in Video Feedback https://www.youtube.com/watch?v=B4Kn3djJMCE https://www.youtube.com/watch?v=B4Kn3djJMCE A film by Jim Crutchfield, Entropy Productions, Santa Cruz (1984). Original U-matic video transferred to digital video. 16 minutes. See: https://csc.ucdavis.edu/~chaos/chaos/films.htm https://csc.ucdavis.edu/~chaos/chaos/films.htm Citation: J. P. Crutchfield, "Space-Time Dynamics in Video Feedback". Physica 10D (1984) 229-245. https://csc.ucdavis.edu/~chaos/chaos/pubs/stdvf-title.html https://csc.ucdavis.edu/~chaos/chaos/pubs/stdvf-title.html Chaotic Attractors of Driven Oscillators https://www.youtube.com/watch?v=Sq8Vu40Bw1g https://www.youtube.com/watch?v=Sq8Vu40Bw1g A film by Jim Crutchfield, Entropy Productions, Santa Cruz (1982). Original 16mm transferred to U-matic video and then to digital video. 13 minutes. In 2022, Crutchfield and his graduate student Kyle Ray described a way to bring the heat production of conventional circuits below the theoretical limit of Landauer's principle by encoding information not as pulses of charge but in the momentum of moving particles. https://www.scientificamerican.com/article/lsquo-momentum-computing-rsquo-pushes-technology-rsquo-s-thermodynamic-limits/ https://www.scientificamerican.com/article/lsquo-momentum-co... While a graduate student, Crutchfield and students from the University of California, Santa Cruz (including Doyne Farmer) built a series of computers that were capable of calculating the motion of a moving roulette ball, predicting which numbers could be excluded from the outcome: The Eudaemonic Pie / Newton's Casino: The Bizarre True Story of How a Band of Physicists and Computer Wizards Took on Las Vegas https://archive.org/details/eudaemonicpie00bass_0/mode/2up https://archive.org/details/eudaemonicpie00bass_0/mode/2up
- bmitc 3y agoThanks for all the references!
- cossatot 3y agoDoes 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.
- IAmGraydon 3y agoIt'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.
- Wolfenstein98k 3y agoCan't be read on mobile (Brave browser)
- alkyon 3y agoHorizontally only;) But the article is well worth it.
- gdubs 3y agoDo yourself a favor and get lost on this website. There's so much great material — for years I've been ending up there after looking for implementation ideas on things like metaballs and isosurfaces, to fractal noise. I love the brutalist simplicity of the site, and the extremely high density of quality information. For those two young to know — this is a taste of what made the early web so exciting.
- danwills 3y agoThis looks like a fractal that's been around for a long time in Fractint and UltraFractal with the name 'Icons'. I believe it's like a generalisation of the well-known 'bifurcation diagram' of the logistic map such that it's got more dimensions, and these images are like slices of it 'through the page'. It makes gorgeous soft and subtle details! Unfortunately since it's essentially a histogram it's tricky to produce high res renderings. Paul Bourke is a total hero of this realm! Great stuff!
- geraldalewis 3y agoI have only seen the first two images, but Paul Bourne + something that looks like non -Abelian sand piles!
- bmitc 3y agoThese are beautiful, but I personally prefer, in an aesthetic sense, the strange attractors that have some asymmetry to them. However, I feel a read-through of the equations and techniques used here will be helpful.
- DonHopkins 3y agoI love how the periodicity of this video spins, locks, then finally lands in chaos: https://twitter.com/crazyclipsonly/status/1690865313770835968 https://twitter.com/crazyclipsonly/status/169086531377083596...