{"id":"urn:lj:livejournal.com:atom1:mathart","title":"Beauty In Mathematics","subtitle":"From Discord, Find Harmony","author":{"name":"Math Art"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom"}},{"@attributes":{"rel":"service.feed","type":"application\/x.atom+xml","href":"https:\/\/mathart.livejournal.com\/data\/atom","title":"Beauty In Mathematics"}}],"updated":"2012-03-12T02:04:57Z","entry":[{"id":"urn:lj:livejournal.com:atom1:mathart:57957","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/57957.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=57957"}}],"title":"Sierpinski Hamantaschen","published":"2012-03-12T02:04:57Z","updated":"2012-03-12T02:04:57Z","content":"http:\/\/seattlelocalfood.com\/2011\/03\/20\/sierpinski-hamantaschen-sierpinskitaschen\/<\/a>

\"the best intersection of math and baking since Pi.\""},{"id":"urn:lj:livejournal.com:atom1:mathart:57696","link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/57696.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=57696"}}],"title":"Batman Equation","published":"2011-10-21T09:20:32Z","updated":"2011-10-21T09:21:16Z","content":"Originally posted by <\/a>just_you_wait<\/b><\/a><\/span>, although there seem to have been some problems with the original image, so I'm trying this instead:


"},{"id":"urn:lj:livejournal.com:atom1:mathart:56970","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/56970.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=56970"}}],"title":"mathart @ 2011-04-07T15:04:00","published":"2011-04-07T18:55:12Z","updated":"2011-04-07T18:55:12Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:56632","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/56632.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=56632"}}],"title":"mathart @ 2011-03-21T19:34:00","published":"2011-03-21T23:25:11Z","updated":"2011-03-21T23:25:11Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:56501","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/56501.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=56501"}}],"title":"This is amazing","published":"2011-03-10T02:20:51Z","updated":"2011-03-10T02:20:51Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:56121","author":{"name":"bntr"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/56121.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=56121"}}],"title":"glider","published":"2011-02-15T19:43:19Z","updated":"2011-02-15T19:43:19Z","content":"Continuous interpretaion of Conway's glider<\/a>

<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:55722","author":{"name":"toxic oxygen"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/55722.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=55722"}}],"title":"favorite mandelbrot zoom (made by someone else)","published":"2010-10-19T09:35:26Z","updated":"2010-10-19T09:36:44Z","content":"But this one in particular deserves more exposure



(higher resolution version here<\/a>)"},{"id":"urn:lj:livejournal.com:atom1:mathart:55512","link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/55512.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=55512"}}],"title":"RIP Benoit Mandelbrot","published":"2010-10-18T22:17:55Z","updated":"2010-10-18T22:20:08Z","content":"Benoit Mandelbrot died last week, aged 85. His groundbreaking work with fractals needs no introduction in this community, and I don't feel qualified to compose a suitable eulogy for the man. I'll resort to linking to one of many obituaries<\/a>, and although it's all but impossible to pick out a definitive visual work, I figured I can't go far wrong with something featuring Jonathan Coulton's song (warning: there's a cuss-word in the chorus)



Does anyone else have any favourite Mandelbrot-inspired images or videos?"},{"id":"urn:lj:livejournal.com:atom1:mathart:54796","author":{"name":"sweepingcolors"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/54796.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=54796"}}],"title":"Domain Coloring","published":"2010-05-14T13:11:44Z","updated":"2010-05-14T14:51:07Z","content":"I've been exploring domain coloring in my Dominium collection ( SweepingColors.com<\/a> ) for almost a year now. If you know of any other websites where I can find drawings like these, please let me know. Thanks.


\"\"<\/a><\/div>"},{"id":"urn:lj:livejournal.com:atom1:mathart:54561","author":{"name":"meche"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/54561.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=54561"}}],"title":"Nature by Numbers","published":"2010-04-07T22:11:35Z","updated":"2010-04-07T22:11:35Z","content":"
<\/div>"},{"id":"urn:lj:livejournal.com:atom1:mathart:54468","author":{"name":"xah lee"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/54468.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=54468"}}],"title":"art exhibition of mathematician Rudy Rucker in San Francisco","published":"2010-04-07T14:11:33Z","updated":"2010-04-07T14:11:33Z","content":"There's a painting exhibition in San Francisco, hosted by Science Fiction in San Francisco (SF in SF), featuring the works of mathematician and science fiction writer Rudy Rucker.

Rudy is famous for his books such as \u201cThe Fourth Dimension\u201d (1984), Infinity and the Mind (1995), and latest non-fiction on cellular automata: The Life Box, The Seshell, and The Soul (2005). amazon

The painting exhibition will be on from April 9 (Friday) to May 22 (Saturday), at Variety Preview Room in San Francisco. (582 Market Street, San Francisco, CA. (415) 781-3893) (View Map)

You're invited to an opening night party on Friday, April 9, from 6 to 9 pm.

In the closing event on Saturday May 22, from 6 to 10 pm, Rudy will read with author Michael Shea.

Paintings and prints will be for sale at the show during the opening and closing events, or online from Rudy's paintings page.

-----------------------

for links and google map, please see my math blog at
http:\/\/xahlee.org\/math\/blog.html<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:54198","author":{"name":"Patrick"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/54198.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=54198"}}],"title":"Check out these ice crystals...","published":"2010-03-28T23:22:00Z","updated":"2010-03-28T23:22:00Z","content":"Check out the ice crystals in this post<\/a> by <\/a>bruevich_mikluh<\/b><\/a><\/span> in <\/a>texture<\/b><\/a><\/span>."},{"id":"urn:lj:livejournal.com:atom1:mathart:53938","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/53938.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=53938"}}],"title":"found on the internet","published":"2010-02-24T22:11:17Z","updated":"2010-02-24T22:11:17Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:53642","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/53642.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=53642"}}],"title":"polynomial roots","published":"2009-12-07T03:13:42Z","updated":"2009-12-07T03:13:42Z","content":"http:\/\/math.ucr.edu\/home\/baez\/week285.html<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:53318","author":{"name":"toxic oxygen"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/53318.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=53318"}}],"title":"domain coloring request (and two images)","published":"2009-11-17T01:25:07Z","updated":"2009-11-17T01:25:07Z","content":"Hi, I'm trying to determine if the following function is modular or not, and



if someone out there could domain color it for me, I'd be most thankful. (tau is in the upper
half plane only, it's zero at rational reals, and I think it's nonconvergent for irrational
reals, but I'm not certain. p_{m} is the mth prime (2,3,5,7,...)

here's something else I'm working on:


<\/center>




<\/center>
<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:52968","author":{"name":"bntr"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/52968.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=52968"}}],"title":"grouping 1-9 elements in sudoku 3x3x3x3 array","published":"2009-11-09T08:45:40Z","updated":"2009-11-09T08:45:40Z","content":"<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:52558","author":{"name":"toxic oxygen"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/52558.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=52558"}}],"title":"ikeda attractor coloring","published":"2009-10-30T22:59:40Z","updated":"2009-10-31T17:50:48Z","content":"
<\/center>




<\/center>




<\/center>


Treat points in the Ikeda attractor as complex numbers, and take
k(z)=f(z)\/1!+f(f(z))\/2!+f(f(f(z)))\/3!+...,
and look that value up on the second image, and plot it on the first.
Where the coloration is clear\/smooth\/solid, you can make a good guess
about where the current point is going to go next. Where it's choppy,
you can't as easily.
<\/a>

EDITED to add: I ended up calculating that pseudoexpoential for
the entire plane in the second image."},{"id":"urn:lj:livejournal.com:atom1:mathart:52014","author":{"name":"Patrick"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/52014.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=52014"}}],"title":"Image Approximation with Genetically Selected Cosines","published":"2009-10-02T18:16:24Z","updated":"2009-10-02T18:18:10Z","content":"

Inspired by <\/a>electrodruid<\/b><\/a><\/span>'s recent post using genetically selected triangles to approximate an image<\/a>, I opted to leverage my recent obsession with Fourier transforms to do Image Approximation with Genetically Selected Cosines<\/a>. That link will take you to my blog with all of the source code and some detailed explanation of the method. If you just want to see the results, you can view the video below.<\/p>\n\n

<\/center>\n\n

Image Approximation with Genetically Selected Cosines<\/a> from Patrick Stein<\/a> on Vimeo<\/a>.<\/center><\/p>"},{"id":"urn:lj:livejournal.com:atom1:mathart:51756","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/51756.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=51756"}}],"title":"found on the internet...","published":"2009-09-28T08:20:05Z","updated":"2009-09-28T08:20:05Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:51694","author":{"name":"Patrick"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/51694.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=51694"}}],"title":"Fourier Transforms of Swarm Data","published":"2009-09-25T21:23:04Z","updated":"2009-09-25T21:23:04Z","content":"

Here are to videos that I created doing inverse Fourier transforms\nof data pulled from a simulated swarm. For more details, see\nthe blog posts linked with each.<\/p>\n\n

\n

Fourier Swarm with Bee Display<\/a> from Patrick Stein<\/a> on Vimeo<\/a>.<\/p>\n

Fourier transform of swarm data with HUD (blog post)<\/a>.<\/p><\/div>\n\n

\n\n

Fourier Swarm<\/a> from Patrick Stein<\/a> on Vimeo<\/a>.<\/p>\n

Inverse Fourier Transform of Swarm Data (blog post)<\/a>.<\/p><\/div>"},{"id":"urn:lj:livejournal.com:atom1:mathart:50974","link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/50974.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=50974"}}],"title":"Digital Darwin","published":"2009-09-15T01:25:33Z","updated":"2009-09-15T01:34:45Z","content":"Some of you may have seen This experiment in genetic programming<\/a>, in which a computer randomly mashes together polygons and selects the most promising looking images based on a fitness function (in this case, how much the resulting image looks like the Mona Lisa).



I saw it at the tail end of last year, was impressed, and promptly forgot about it. Yesterday I remembered it for some reason, and tonight I wrote my own implementation, albeit one which uses circles rather than arbitrary polygons. This year is the 150th anniversary of Charles Darwin's birth, and he's been in the news for various reasons recently, not least because there's apparently a movie coming out about him. He's a pretty distinctive character, and given that my current implementation only works in greyscale, I chose a black & white photograph of him as my test. My program hasn't been running too long (in the grand scheme of things - these kind of programs can take a while to develop the finer details), but I thought I'd show you what I've got so far:

<\/a>

I'm not too hot on the terminology, but I know that there are people that argue that this is not a genetic algorithm, and I'm inclined to agree (although I don't know what to call it, exactly). There is no \"breeding\" between the fittest images - I simply take the current image, generate 10 more (each of which comes from making one random change: adding\/removing of circles, or changing their size, position or transparency), and choose the \"fittest\" to asexually reproduce in the next generation. Although in Alsing's original, he allowed for the possibility that if a \"parent\" image produced \"child\" images which were all worse than the original then the parent stays until the next iteration, I've found that the picture seems to come together more quickly if I let the parent die, even if all of its offspring are weaker. Perhaps it helps to overcome some of the local maxima of what's basically a hill climbing algorithm<\/a>.

Anyway, it's a cool thing to play about with, even if it's not new. It was surprisingly easy to implement, and I have some ideas for improving the program in ways which are a bit different to what's been tried by other variations on Alsing's technique, so I might have a few more of these to show at some point."},{"id":"urn:lj:livejournal.com:atom1:mathart:50810","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/50810.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=50810"}}],"title":"found on the internet...","published":"2009-09-08T04:46:12Z","updated":"2009-09-08T04:46:12Z","content":""},{"id":"urn:lj:livejournal.com:atom1:mathart:50367","author":{"name":"jefster the jester"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/50367.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=50367"}}],"title":"mathart @ 2009-06-16T01:10:00","published":"2009-06-16T05:06:06Z","updated":"2009-06-16T05:06:06Z","content":"see here<\/a>"},{"id":"urn:lj:livejournal.com:atom1:mathart:50078","author":{"name":"toxic oxygen"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/50078.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=50078"}}],"title":"mandelbrot set art","published":"2009-02-11T21:04:28Z","updated":"2009-02-11T21:04:28Z","content":"blargh, coralcache doesn't seem to like me, so no movie today, but:

<\/center>

(it was made by combining this<\/a>, and this<\/a>)"},{"id":"urn:lj:livejournal.com:atom1:mathart:49740","author":{"name":"toxic oxygen"},"link":[{"@attributes":{"rel":"alternate","type":"text\/html","href":"https:\/\/mathart.livejournal.com\/49740.html"}},{"@attributes":{"rel":"self","type":"text\/xml","href":"https:\/\/mathart.livejournal.com\/data\/atom\/?itemid=49740"}}],"title":"continued fractions from binary representations of numbers","published":"2009-02-07T00:59:02Z","updated":"2009-02-07T00:59:02Z","content":"take the bits from the binary digit of a number x in the unit interval
and use them to construct a continued fraction.

the result (as a function of x) looks something like this:


<\/center>
<\/a>"}]}