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### seeking for "beautiful" formula

Aug 11 2013 | 8:32 am

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)

Aug 11 2013 | 1:56 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 | 2:01 pm

jez, it is tool long, thats why i had trouble posting it to the forum with a link title.

Aug 11 2013 | 2:01 pm

jit.gen.superformula?

Aug 11 2013 | 2:38 pm

Maybe not mathematically beautiful, but this is impressive nonetheless!

Aug 11 2013 | 3:30 pm

now that would be worth to make it an abstraction.

Aug 11 2013 | 3:35 pm

and there is some space to fill on wolfram, too:

http://www.wolframalpha.com/input/?i=donald+duck+equation

Aug 11 2013 | 4:36 pm

e^(i*pi)+1=0

Aug 13 2013 | 8:06 am

Strange Attractors:
Creating Patterns in Chaos
http://sprott.physics.wisc.edu/sa.htm

Aug 13 2013 | 2:51 pm

With all due respect, it’s the *mapping* that’s the central issue rather than the algorithm, IMHO.

Aug 13 2013 | 9:27 pm

"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 13 2013 | 11:55 pm

e^(i*pi)+1=0

You stole my thunder.

Aug 14 2013 | 1:44 am

@woyteg
+1 for GEB

Aug 14 2013 | 3:22 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 | 4:16 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…

— Pasted Max Patch, click to expand. —
Aug 15 2013 | 4:34 am

a good formula is good mapping of (x)

Aug 15 2013 | 6:22 am

> looking for "beautiful" formula.

aren’t we all?

Aug 15 2013 | 6:23 am

and what’s beautiful anyway?

Aug 15 2013 | 6:28 am

and what’s beautiful anyway?

responses are disabled until this question is cleared

Aug 15 2013 | 6:54 am

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.

Aug 15 2013 | 9:12 am

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 | 12:51 am

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)

Aug 16 2013 | 4:41 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.

Perlin noise flow field ? http://www.andysaia.com/radicalpropositions/perlin-noise-flow-fields/

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