seeking for "beautiful" formula

Aug 11, 2013 at 8:32am

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

#258587
Aug 11, 2013 at 1:56pm

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

#258601
Aug 11, 2013 at 2:01pm

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

#258602
Aug 11, 2013 at 2:01pm

jit.gen.superformula?

#258603
Aug 11, 2013 at 2:38pm

Maybe not mathematically beautiful, but this is impressive nonetheless!

#258608
Aug 11, 2013 at 3:30pm

now that would be worth to make it an abstraction.

#258611
Aug 11, 2013 at 3:35pm

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

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

#258612
Aug 11, 2013 at 4:36pm

e^(i*pi)+1=0

#258614
Aug 13, 2013 at 8:06am

Strange Attractors:
Creating Patterns in Chaos

http://sprott.physics.wisc.edu/sa.htm

#258771
Aug 13, 2013 at 2:51pm

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

#258812
Aug 13, 2013 at 9:27pm

“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

#258846
Aug 13, 2013 at 11:55pm

e^(i*pi)+1=0

You stole my thunder.

#258851
Aug 14, 2013 at 1:44am

@woyteg
+1 for GEB

A fun read!

#258854
Aug 14, 2013 at 3:22am

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

#258860
Aug 15, 2013 at 4:16am

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. –
#258956
Aug 15, 2013 at 4:34am

a good formula is good mapping of (x)

#258959
Aug 15, 2013 at 6:22am

> looking for “beautiful” formula.

aren’t we all?

#258975
Aug 15, 2013 at 6:23am

and what’s beautiful anyway?

#258976
Aug 15, 2013 at 6:28am

and what’s beautiful anyway?

responses are disabled until this question is cleared

#258979
Aug 15, 2013 at 6:54am

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:

https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-frc3/q71/995963_10151843715718478_384460375_n.jpg

#258983
Aug 15, 2013 at 9:12am

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.

#259001
Aug 16, 2013 at 12:51am

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)

#259047
Aug 16, 2013 at 4:41am

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/

#259061

You must be logged in to reply to this topic.