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Intriguing... that they are antialiased is even more impressive (supersampling?)
You're a genuous!! Aside from the pun, what if you set some equations equal to values close to zero, but not exactly, and compare the graphs you get to the zero set equations.
Should be hanging in The Museum of Modern Art!
my god, this is just plain cool:
yep, there we are: http://denvish.net/ulf/090807/48788_laserrend.php
the narrowing in of boxes looks cool, but the only reason it 'narrows' in is because i am rendering the graphs at different accuracies, it draws a box whenever it detects that the graph passes through it. so having different accuracies, different sized boxes, they congrugate around where the graph parts are drawn
A good technique, a bit like my "brute force" method would you say? But some kind of brute force may be the only way, as the function could pop up anywhere.
ive figured out a good method that renders the objects perfectly, at arbitrary depth, and works for any implicit function http://denvish.net/ulf/090807/33048_laser.php i absolutely adore the second graph, and third graph is just immense  thinking about it, this could be directly extended into 3D aswell, only you would have a few more cases to check for, but otherwise it is directly extendable
You could go about graphing it in 3D, storing only those points which satisfy the requirement = 0. The important thing when doing this is to build in a "step size" parameter allowing you to get approximations first.
Ideas off the top of my head:
Ive been thinking, how would one go about rendering an implict 2d polynomial graph? 