peterchang

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.

https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/q71/601991_10151831632593478_682930029_n.jpg

https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-ash4/q71/999412_10151831632723478_165626781_n.jpg

https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-frc1/q71/1001240_10151831632733478_1231132565_n.jpg

https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-ash3/q71/1150831_10151835705133478_1608384247_n.jpg

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-prn1/q71/31479_10151835705508478_432534851_n.jpg

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


seeking-for-beautiful-formula

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.

Maybe not mathematically beautiful, but this is impressive nonetheless!


now that would be worth to make it an abstraction.

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

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

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

"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


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...

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...

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.

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

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


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.

good mapping of X is boring and not art at all. 

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

here's a few of those that I implemented in Max in 2012:

(includes: butterfly curve, Lemniscate of Bernoulli, hypocycloid, diamond curve, Lituus spiral, SuperShape)

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)


http://blog.visual.ly/45-ways-to-communicate-two-quantities/

http://moebio.com/research/FatFontsPlayer/

those two show how what is mapped cna change everything.

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

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/


seeking for "beautiful" formula