does anyone know a website with maths functions that are gonna make cool patterns?

like, i know (x squared + y squared = z) is gonna make a circle

but does anyone know a site where i can see a list of such functions and the shapes they produce?

the circle one isn't even a function, techically...but ya's all know what i mean right?

i'm not sure exactly what you're after, but one thing your post brought to my mind was parametric equations...e.g.

t) = sin t
y(t) = cos t

where x and y are functions of t. you can plot x and y on a coordinate plane where t itself can be a function of time, or just a changing angle (theta?). the above function, for 0 < t < 2pi will generate a circle. by varying t) and y(t), you can come up with different geometrical shapes, however usually you just get crazy curves that can look pretty cool.

i used parametric equations in a GEM visualisation i made. it was model after the pix_data simple example. instead of using random X and Y pairs, i replaced the random function with a parametric equation so that the picture was 'traced' over a curvy pattern. (actually i added a very small random number to the X and Y coordinates generated by the parametric equation to blur the curve a little bit, and i rotate the curve by X degrees where X is a function of time...but that's besides the point). parametic curves can 'look good'...i am not sure about them 'sounding good' but it's something to try out.

hope this helps. if you want ideas for some interesting parametric curve equations let me know.

--zac hilbert~

i should note that the parametric equation about yields a true circle only if you are working with a square pixel ratio. if the pixel ration is not square, you multiply either the x or y function by the aspect ratio...or is it divide...whatever...to get get a circle.

hilbert~

[url=http://cm.socialgeek.com/avs.html ]http://cm.socialgeek.com/avs.html

Some nice equations with pictures., implemented in Winamp 2.81's AVS system. Mostly iterative equations, like F(x,y)->(x2,y2), repeat over and over to get more points (feedback). Not curves, individual points jump about a lot, but the envelope (attractor) of the points forms a pattern.

Gridlflow is fun for visual feefback loops, check out the "goop" examples on http://gridflow.ca or really pretty much any of the gridflow examples, they all use maths to make cool pictures..


x = A sin ( t )
y = B cos ( t )

is an ellipse, but try

x = sin ( A t )
y = cos ( B t )

too, start with small integer values for A and B and see what happens when you change them...

I'm updating my website currently - so this link is broken:

http://cm.socialgeek.com/avs.html

The new permanent link is:

[url=http://cm.socialgeek.com/index.php?page=coding/winamp-avs/about ]http://cm.socialgeek.com/index.php?page=coding/winamp-avs/about

(I tried editing my post, but no joy)

oh claudius... i hate your website. i always end up getting stuck on the thing about the bananas

anyway...cheers everyone 4 the links. also thanks for expanding my vocab. to my previously misused "function", i can know add new words such as "parametric equations" and "iterative equations"...no doubt i will be misusing these too in the near future.

wow, fuck the bananas....finally got past them...and these patterns are neat. hopefully i can get some of this stuff to work in pd too.