Comments on: mathematic mandalas
http://www.metafilter.com/192632/mathematic-mandalas/
Comments on MetaFilter post mathematic mandalasTue, 14 Sep 2021 08:17:47 -0800Tue, 14 Sep 2021 08:17:47 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60mathematic mandalas
http://www.metafilter.com/192632/mathematic-mandalas
<a href="https://www.youtube.com/watch?v=qhbuKbxJsk8">Times Tables, Mandelbrot and the Heart of Mathematics [slyt]</a> post:www.metafilter.com,2021:site.192632Tue, 14 Sep 2021 08:17:11 -0800dhruvamathematicaMandelbrottimestableBy: dhruva
http://www.metafilter.com/192632/mathematic-mandalas#8147712
<small>cortex bait </small>comment:www.metafilter.com,2021:site.192632-8147712Tue, 14 Sep 2021 08:17:47 -0800dhruvaBy: Acey
http://www.metafilter.com/192632/mathematic-mandalas#8147727
Related: <a href="https://youtu.be/FFftmWSzgmk">What's so special about the Mandelbrot Set? (Numberphile)</a>comment:www.metafilter.com,2021:site.192632-8147727Tue, 14 Sep 2021 09:45:34 -0800AceyBy: BobTheScientist
http://www.metafilter.com/192632/mathematic-mandalas#8147741
Whoa, you and Matt Henderson must love each other very much. <a href="https://www.youtube.com/watch?v=vU-g6mC1F0g"> Posted today on Numberphile</a>: planetary orbits sweep out similar pics.comment:www.metafilter.com,2021:site.192632-8147741Tue, 14 Sep 2021 11:04:30 -0800BobTheScientistBy: stinkfoot
http://www.metafilter.com/192632/mathematic-mandalas#8147747
<a href="https://www.youtube.com/watch?v=56gzV0od6DU">I like this intro video on the Mandelbrot Set</a>, and in particular the line at 1:05
"IBM was looking for creative thinkers, non-conformists, even rebels... people like Benoit Mandelbrot"
So sexy.comment:www.metafilter.com,2021:site.192632-8147747Tue, 14 Sep 2021 11:21:15 -0800stinkfootBy: geoff.
http://www.metafilter.com/192632/mathematic-mandalas#8147757
Mandelbrot and fractals are really interesting. His description of the coastline of Britain is something I use a lot to describe problems of measurement, though I probably am bastardizing his original intent. I enjoyed "Misbehavior of the Markets" and his fascination of financial instruments to describe fractals and vice versa. Ignore the Taleb co-authorship if you want, the text is good and not trying to really be a business book at all.
One thing about the Mandelbrot set is that it has a lot of "wow neat!" factors built in but I feel like it might be the mathematical equivalent of an optical illusion. I'm not saying it isn't valid, just that it doesn't seem to predict things or have any real uses outside of theoretical mathematics. If you look up practical uses of fractals it is a bit hand wavy beyond using fractals in computer graphics to generate realistic scenery but hopefully I'm wrong?comment:www.metafilter.com,2021:site.192632-8147757Tue, 14 Sep 2021 11:52:13 -0800geoff.By: Hairy Lobster
http://www.metafilter.com/192632/mathematic-mandalas#8147763
I think there's a few practical uses worth mentioning such as <a href="https://en.wikipedia.org/wiki/Fractal_antenna">fractal antennas</a> and <a href="https://www.arifractal.net/technologies/fractal-fluid-control/fractal-mixing/">fractal fluid mixers</a>.comment:www.metafilter.com,2021:site.192632-8147763Tue, 14 Sep 2021 12:03:58 -0800Hairy LobsterBy: BungaDunga
http://www.metafilter.com/192632/mathematic-mandalas#8147764
Just calculating something's <a href="https://en.wikipedia.org/wiki/Fractal_dimension#Estimating_from_real-world_data">fractal dimension</a> has been a trend recently, and it may tell you something about the dynamics of the system in question. eg if it turns out images of tumors have different fractal dimension from ordinary tissue, it might be a useful diagnostic measure. There's a paper on <a href="https://cpb-us-e1.wpmucdn.com/blogs.uoregon.edu/dist/e/12535/files/2015/12/PollockPRL-1gq9u97.pdf">analyzing and authenticating Pollock paintings with fractal dimension</a>.comment:www.metafilter.com,2021:site.192632-8147764Tue, 14 Sep 2021 12:12:19 -0800BungaDungaBy: BungaDunga
http://www.metafilter.com/192632/mathematic-mandalas#8147765
There was also some attempts at <a href="https://en.wikipedia.org/wiki/Fractal_compression">fractal compression algorithms</a> but they haven't been shown to be practical.comment:www.metafilter.com,2021:site.192632-8147765Tue, 14 Sep 2021 12:13:42 -0800BungaDungaBy: kjs3
http://www.metafilter.com/192632/mathematic-mandalas#8147820
<em>If you look up practical uses of fractals it is a bit hand wavy beyond using fractals in computer graphics to generate realistic scenery but hopefully I'm wrong?</em>
In addition to generating natural looking computer generated environments and the above mentioned fractal antenna tech important to space-limited uses (e.g. RFID, cell phones), fractals have been commercialized in image compression. They're also useful for modeling certain types of real-world dynamic systems including Brownian motion.
A search for "iterated function systems" might give more examples.
<em>There was also some attempts at fractal compression algorithms but they haven't been shown to be practical.</em>
You might actually read that link. A number of companies shipped actual, working fractal (de)compression implementations (usually licensed from Iterated Systems, Inc.), perhaps most notably Microsoft used fractal compression in its Encarta encyclopedia. There were limitations with the tech (it's *extremely* compute intensive to compress images, but very, very fast to decompress), but it certainly fits most definitions of 'practical'.
Disclaimer: I worked in Drs. Barnsley & Sloan's IFS lab in the 80s before they started Iterated Systems.comment:www.metafilter.com,2021:site.192632-8147820Tue, 14 Sep 2021 13:08:07 -0800kjs3By: eviemath
http://www.metafilter.com/192632/mathematic-mandalas#8147827
There's some important and useful connections between fractals and wavelets (via iterated function systems/discrete dynamical systems), too. And wavelets of course have tons of uses outside theoretical math. Thing is, not every fractal set look fractaly, like the Mandelbrot set. Just subdividing a square into subsquares, but doing so over and over and over again, technically gives you a fractal.comment:www.metafilter.com,2021:site.192632-8147827Tue, 14 Sep 2021 13:25:25 -0800eviemathBy: BungaDunga
http://www.metafilter.com/192632/mathematic-mandalas#8147835
<em>it certainly fits most definitions of 'practical'</em>
Oh, yes, and I'd even known about the Encarta thing. I should have said that fractal compression hasn't found popularity compared to other methods.comment:www.metafilter.com,2021:site.192632-8147835Tue, 14 Sep 2021 13:34:03 -0800BungaDungaBy: atomicstone
http://www.metafilter.com/192632/mathematic-mandalas#8147906
Just makes me hungry for <a href="https://www.google.com/search?q=mandelbrot+recip3&client=ms-android-verizon&sxsrf=AOaemvLysI06vIoU2MQ6wA3CdwzSWahV2Q%3A1631661057219&ei=ASxBYajrDKePxc8PsrqX4AM&oq=mandelbrot+recip3&gs_lcp=ChNtb2JpbGUtZ3dzLXdpei1zZXJwEAMyBwgjELACECcyBAgAEA0yBAgAEA0yBAgAEA0yBggAEA0QHjIGCAAQDRAeMgYIABANEB4yBggAEA0QHjoECAAQRzoECCMQJzoNCAAQgAQQhwIQsQMQFDoECAAQQzoFCAAQgAQ6CggAEIAEEIcCEBQ6BggAEBYQHlDdVFjXXGCkZWgAcAF4AIAB2QGIAZAGkgEFNC4yLjGYAQCgAQHIAQjAAQE&sclient=mobile-gws-wiz-serp">dessert</a>.comment:www.metafilter.com,2021:site.192632-8147906Tue, 14 Sep 2021 16:12:23 -0800atomicstoneBy: crossswords
http://www.metafilter.com/192632/mathematic-mandalas#8147925
Mathologer is great, super accessible recreational maths!
Jumping on the cool fractal train, I'm fairly sure that google maps still uses a Hilbert curve to encode geospatial data. I found <a href="https://blog.christianperone.com/2015/08/googles-s2-geometry-on-the-sphere-cells-and-hilbert-curve/">a blog</a> that talks about an earlier version of their package. Because the Hilbert curve both fills space and has some fractal stuff going on, it has nice properties for storing data about 2D things in a 1D array. In particular because nearby areas in space tend to also be near each other along the curve.comment:www.metafilter.com,2021:site.192632-8147925Tue, 14 Sep 2021 16:59:42 -0800crossswordsBy: BungaDunga
http://www.metafilter.com/192632/mathematic-mandalas#8147927
<a href="https://www.evilmadscientist.com/2008/sierpinski-cookies/">dessert, you say</a>?comment:www.metafilter.com,2021:site.192632-8147927Tue, 14 Sep 2021 17:03:18 -0800BungaDungaBy: aniola
http://www.metafilter.com/192632/mathematic-mandalas#8147972
<em>I'm not saying it isn't valid, just that it doesn't seem to predict things or have any real uses outside of theoretical mathematics.</em>
I thought fractals were, like, all over the place in nature, which is not at all theoretical and really actually quite practical?comment:www.metafilter.com,2021:site.192632-8147972Tue, 14 Sep 2021 20:02:16 -0800aniolaBy: Harvey Kilobit
http://www.metafilter.com/192632/mathematic-mandalas#8147988
HEY EVERYONE do you want to hear my Mandelbrot joke?
Q: What does the "B." stand for in the name Benoit B. Mandelbrot?
A: Benoit B. Mandelbrotcomment:www.metafilter.com,2021:site.192632-8147988Tue, 14 Sep 2021 20:57:59 -0800Harvey KilobitBy: flabdablet
http://www.metafilter.com/192632/mathematic-mandalas#8148001
<em>I thought fractals were, like, all over the place in nature</em>
<a href="https://www.goodreads.com/book/show/64582.Chaos">Others agree.</a>comment:www.metafilter.com,2021:site.192632-8148001Tue, 14 Sep 2021 22:35:24 -0800flabdabletBy: storybored
http://www.metafilter.com/192632/mathematic-mandalas#8148240
<em>Q: What does the "B." stand for in the name Benoit B. Mandelbrot?
A: Benoit B. Mandelbrot</em>
Rats, I was going to say "the national anthem"comment:www.metafilter.com,2021:site.192632-8148240Wed, 15 Sep 2021 13:41:09 -0800storybored