Thursday, February 17, 2011

Look, Ma, NO Fractals...No, Wait !

Fractal Wada Basin 2 by Luc2
If that's not the most beautiful mathematical "computer art" artwork you've ever seen, show me another.

It looks like three perfectly mirrored spheres, on a gridded plane with rectangles, under a cloudy sky. Actually if you look closer, it's FOUR (tetra) such spheres, packed, the centers of which form a tetrahedron, simplest of the five Platonic solids, when connected.

With such simplicity, and other than the clouds, there is no fractility, yes?

Yes? No. Look closer. Click twice on the picture to superenfractinate.

I mean GEEZ, don't those look like Julia sets? What is THAT all about ?

(and yah, I know we're talking about the field that is  Projective Geometry )

I do not choose to analyze this beautiful computer art at this time other than PG though I do look forward to doing so, as did Paul Dirac, but by all means feel free to offer your own thoughts. I think that this one artwork is so good first for its beauty that it needs no explanation, but second for the the thousands of mathematical ideas it can launch.

So ... enjoy.

And honor the artist Luc2 please, by looking at his other work, which you can find by clicking:  here .


Steven Colyer said...

I would REALLY like to know if making artwork like that is possible on a PC, and if so I'd like to make some. My parents were brilliant but knew nothing about Math or Science, being the first-rate artists that they were (in fact they met at America's top art school, at the time they met).

If nothing else, I'd like to make that sky a sunset with some red thrown in, and see what that does to the fractals in the tetraspheres.

Yeah, that's just like an engineer, huh? Looks at something that works perfectly well, enjoys it for a day, and then his thoughts turn to how it can be improved. :-)

We're never happy. :-(

Jérôme CHAUVET said...

To answer your question : yes, this is possible to make images like that on a pc. You need a raytracer. To do so, you will need a rendering program which calculates the trajectory of virual ray of light, the so-called "ray-tracer". Then put in the "filmed" space 2 infinite parallel planes mapped with nice graphics + 4 spheres (algebraic equations are enough). Reflections are easily calculated with such a rendering algorithm. It's then just a matter of time if you can calculate more complicated pictures...


Steven Colyer said...

Thanks, Jérôme. Can you name a specific program, or provide a link? One that doesn't suck up half the memory on my 'puter? much obliged if so.

Jérôme CHAUVET said...

I recommend using Blender. This 3D modelling software is a freeware, which has an embedded ray-tracer.

It requires a little bit of training, but NOT TOO MUCH if you just try and create simple objects like planes, spheres, cubes, and so on... You can view tutorials on U-tube if needed.

There are other such freewares, which I however never tried in the past.


Bill Newbold said...

I like to think neither inside the box nor outside the box I become the box. And I am a box... :)
I helped with ray tracing back in 1988 in college,.. nobody knew what we were doing back then,..