Implicit surfaces

[lycium]

2. Render some 3D fractals with Indigo

the normal is everywhere the gradient of this potential function.

Hmmm... How do you define the gradient of a fractal?

With great difficulty, as you can imagine... actually, there are ways to do it analytically, without finite difference (as I do), however this needs per-equation analysis and I wanted it to work with "black box" point-sampled potential functions.

[galinette]

With great difficulty, as you can imagine... actually, there are ways to do it analytically, without finite difference (as I do), however this needs per-equation analysis and I wanted it to work with "black box" point-sampled potential functions.

In the case of a fractal, the gradient does not exist mathematically! (derivatives doesn't exist)

[lycium]

Some clever mathematicians worked that out, and recently there's a nice blog series on doing this for the Mandelbulb as a particularly well analysed example: http://blog.hvidtfeldts.net/index.php/2 ... ximations/

[galinette]

Some clever mathematicians worked that out, and recently there's a nice blog series on doing this for the Mandelbulb as a particularly well analysed example: http://blog.hvidtfeldts.net/index.php/2 ... ximations/

That's an approximation based on finite resolution. True fractals have no definable normal (Not only it cannot be calculated analytically, it does not exist)

However, it seems quite interesting for making 3d images, that's true... Refining the fractal resolution below visible wavelength range would not mean anything anyway...

Don't tell me that clever mathematicians have found an exact decimal form of Pi, or a tesselation of a sphere with a finite number of triangles

[lycium]

We don't even have true real numbers and infinite image resolution, so why should we expect normals to true fractals?

[PureSpider]

Translation for regular human beings: "BRAIN HADUOKEN!"

[CTZn]

Haxors !!!