mathematic mandalas
September 14, 2021 8:17 AM Subscribe
Related: What's so special about the Mandelbrot Set? (Numberphile)
posted by Acey at 9:45 AM on September 14, 2021 [2 favorites]
posted by Acey at 9:45 AM on September 14, 2021 [2 favorites]
Whoa, you and Matt Henderson must love each other very much. Posted today on Numberphile: planetary orbits sweep out similar pics.
posted by BobTheScientist at 11:04 AM on September 14, 2021
posted by BobTheScientist at 11:04 AM on September 14, 2021
I like this intro video on the Mandelbrot Set, and in particular the line at 1:05
"IBM was looking for creative thinkers, non-conformists, even rebels... people like Benoit Mandelbrot"
So sexy.
posted by stinkfoot at 11:21 AM on September 14, 2021
"IBM was looking for creative thinkers, non-conformists, even rebels... people like Benoit Mandelbrot"
So sexy.
posted by stinkfoot at 11:21 AM on September 14, 2021
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?
posted by geoff. at 11:52 AM on September 14, 2021
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?
posted by geoff. at 11:52 AM on September 14, 2021
I think there's a few practical uses worth mentioning such as fractal antennas and fractal fluid mixers.
posted by Hairy Lobster at 12:03 PM on September 14, 2021 [2 favorites]
posted by Hairy Lobster at 12:03 PM on September 14, 2021 [2 favorites]
Just calculating something's fractal dimension 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 analyzing and authenticating Pollock paintings with fractal dimension.
posted by BungaDunga at 12:12 PM on September 14, 2021
posted by BungaDunga at 12:12 PM on September 14, 2021
There was also some attempts at fractal compression algorithms but they haven't been shown to be practical.
posted by BungaDunga at 12:13 PM on September 14, 2021
posted by BungaDunga at 12:13 PM on September 14, 2021
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?
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.
There was also some attempts at fractal compression algorithms but they haven't been shown to be practical.
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.
posted by kjs3 at 1:08 PM on September 14, 2021 [3 favorites]
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.
There was also some attempts at fractal compression algorithms but they haven't been shown to be practical.
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.
posted by kjs3 at 1:08 PM on September 14, 2021 [3 favorites]
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.
posted by eviemath at 1:25 PM on September 14, 2021 [3 favorites]
posted by eviemath at 1:25 PM on September 14, 2021 [3 favorites]
it certainly fits most definitions of 'practical'
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.
posted by BungaDunga at 1:34 PM on September 14, 2021 [1 favorite]
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.
posted by BungaDunga at 1:34 PM on September 14, 2021 [1 favorite]
Just makes me hungry for dessert.
posted by atomicstone at 4:12 PM on September 14, 2021 [2 favorites]
posted by atomicstone at 4:12 PM on September 14, 2021 [2 favorites]
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 blog 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.
posted by crossswords at 4:59 PM on September 14, 2021
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 blog 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.
posted by crossswords at 4:59 PM on September 14, 2021
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.
I thought fractals were, like, all over the place in nature, which is not at all theoretical and really actually quite practical?
posted by aniola at 8:02 PM on September 14, 2021
I thought fractals were, like, all over the place in nature, which is not at all theoretical and really actually quite practical?
posted by aniola at 8:02 PM on September 14, 2021
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. Mandelbrot
posted by Harvey Kilobit at 8:57 PM on September 14, 2021 [6 favorites]
Q: What does the "B." stand for in the name Benoit B. Mandelbrot?
A: Benoit B. Mandelbrot
posted by Harvey Kilobit at 8:57 PM on September 14, 2021 [6 favorites]
I thought fractals were, like, all over the place in nature
Others agree.
posted by flabdablet at 10:35 PM on September 14, 2021
Others agree.
posted by flabdablet at 10:35 PM on September 14, 2021
Q: What does the "B." stand for in the name Benoit B. Mandelbrot?
A: Benoit B. Mandelbrot
Rats, I was going to say "the national anthem"
posted by storybored at 1:41 PM on September 15, 2021 [1 favorite]
A: Benoit B. Mandelbrot
Rats, I was going to say "the national anthem"
posted by storybored at 1:41 PM on September 15, 2021 [1 favorite]
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posted by dhruva at 8:17 AM on September 14, 2021