seeking for "beautiful" formula
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
https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-prn1/q71/31479_10151835705508478_432534851_n.jpg
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
jez, it is tool long, thats why i had trouble posting it to the forum with a link title.
jit.gen.superformula?
now that would be worth to make it an abstraction.
and there is some space to fill on wolfram, too:
e^(i*pi)+1=0
Strange Attractors:
Creating Patterns in Chaos
http://sprott.physics.wisc.edu/sa.htm
With all due respect, it's the *mapping* that's the central issue rather than the algorithm, IMHO.
"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
e^(i*pi)+1=0
You stole my thunder.
@woyteg
+1 for GEB
A fun read!
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
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...
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a good formula is good mapping of (x)
> looking for “beautiful” formula.
aren't we all?
and what's beautiful anyway?
and what’s beautiful anyway?
responses are disabled until this question is cleared
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.
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.
lots of examples of aesthetically pleasing math via
http://paulbourke.net/geometry/
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)
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.
Perlin noise flow field ? http://www.andysaia.com/radicalpropositions/perlin-noise-flow-fields/