seeking for "beautiful" formula


    Aug 11 2013 | 3:32 pm
    anyone know any "beautiful" formula ??
    i am working for my dissertation, and looking for "beautiful" formula.
    so far I have done 6 degree polynomial and Lorenz attractor, and need more great and impressive formula.
    (can be differential equations too)
    some picture:
    1)Lorens attractor
    https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/q71/601991_10151831632593478_682930029_n.jpg
    2)Lorens attractor
    https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-ash4/q71/999412_10151831632723478_165626781_n.jpg
    3)Lorens attractor
    https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-frc1/q71/1001240_10151831632733478_1231132565_n.jpg
    4)polynomial
    https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-ash3/q71/1150831_10151835705133478_1608384247_n.jpg
    5)polynomial

    • Aug 11 2013 | 8:56 pm
      http://www.wolframalpha.com/input/?i=PolarPlot%5B(1+%2B+0.9+Cos%5B8+t%5D)+(1+%2B+0.1+Cos%5B24+t%5D)+(0.9+%2B+0.05+Cos%5B200+t%5D)+(1+%2B+Sin%5Bt%5D),+%7Bt,+-Pi,+Pi
    • Aug 11 2013 | 9:01 pm
      jez, it is tool long, thats why i had trouble posting it to the forum with a link title.
    • Aug 11 2013 | 9:01 pm
      jit.gen.superformula?
    • Aug 11 2013 | 9:38 pm
      Maybe not mathematically beautiful, but this is impressive nonetheless!
    • Aug 11 2013 | 10:30 pm
      now that would be worth to make it an abstraction.
    • Aug 11 2013 | 10:35 pm
      and there is some space to fill on wolfram, too:
    • Aug 11 2013 | 11:36 pm
      e^(i*pi)+1=0
    • Aug 13 2013 | 3:06 pm
      Strange Attractors:
      Creating Patterns in Chaos
    • Aug 13 2013 | 9:51 pm
      With all due respect, it's the *mapping* that's the central issue rather than the algorithm, IMHO.
    • Aug 14 2013 | 4:27 am
      "The mapping is the message"! But primitive mapping of interesting input might get interesting too :)
      Anyway "Gödel Escher Bach" might be an interesting book there too
    • Aug 14 2013 | 6:55 am
      e^(i*pi)+1=0
      You stole my thunder.
    • Aug 14 2013 | 8:44 am
      @woyteg
      +1 for GEB
      A fun read!
    • Aug 14 2013 | 10:22 am
      given that one could argue that any artistic praxis is an exercise in mapping /translation, you could possibly hypothesise that all good art is just good mapping; all bad art is bad mapping... ;-]
      edit: replace 'good' with 'beautiful', 'bad' with 'ugly' etc etc ie boring/interesting, smooth/abrasive
      note to self stop posting on forums after dinner
    • Aug 15 2013 | 11:16 am
      I figure this is a good opportunity to learn about [expr]. I should have listened more in school. Maybe if they taught math like this I would have paid attention...
      -
    • Aug 15 2013 | 11:34 am
      a good formula is good mapping of (x)
    • Aug 15 2013 | 1:22 pm
      > looking for “beautiful” formula.
      aren't we all?
    • Aug 15 2013 | 1:23 pm
      and what's beautiful anyway?
    • Aug 15 2013 | 1:28 pm
      and what’s beautiful anyway?
      responses are disabled until this question is cleared
    • Aug 15 2013 | 1:54 pm
      Thx for reply for everyone, these reply helps me a lot, and i am trying to demonstrate "e^(i*pi)+1=0" and Donal duck equ.
      I am working for my project, which is to show people about the art, the beautiful in MATHS. I am looking for if there is some adjective to describe what beauty is.
      It is hard to describe, but I would say it look nature.
      this is my example:
    • Aug 15 2013 | 4:12 pm
      good mapping of X is boring and not art at all.
      unless you are mapping X using [expr ($i1+0)*1], or course. becasue this will end up as a quite astounding and progressive piece of minimalism.
      in this case i would suggest that X should be in a range of 1 - 1 to avoid that displaying the parameter movement in the GUI object becomes too irritating for the eyes.
    • Aug 16 2013 | 7:51 am
      lots of examples of aesthetically pleasing math via
      here's a few of those that I implemented in Max in 2012:
      http://bit.ly/geom_dev
      (includes: butterfly curve, Lemniscate of Bernoulli, hypocycloid, diamond curve, Lituus spiral, SuperShape)
    • Aug 16 2013 | 11:41 am
      not so long ago i stumbled across this http://blog.visual.ly/45-ways-to-communicate-two-quantities/
      and, there's that related page http://moebio.com/research/FatFontsPlayer/
      those two show how what is mapped cna change everything.