[PD] Colored (fractal, 1/f^a) noise generator for PD

[Mathieu Bouchard]

On Sun, 20 Aug 2006, Martin Peach wrote:

>> Then by this standard, the 1/x function is self-similar, and so are all 
>> hyperbolas. That is, as long as similarity is defined as modulo the group 
>> of diagonal matrices conjugated by rotation matrices.
> I don't see that. Zooming in and out of 1/x or a hyperbola just makes the 
> curve look bigger or smaller, whereas noise looks the same at all scales.

What? No, you have to zoom out the x while you zoom in the y by the same 
amount, or the other way around. The product of the zoom factors of x and 
y should be 1.

> "A fractal is by definition a set for which the Hausdorff Besicovitch 
> dimension strictly exceeds the topological dimension"

I stand corrected.

> "However, a fractal may have an integer D ... the trail of Brownian 
> motion is fractal because D=2, while Dt=1" (i.e. a randomly meandering 
> line will eventually completely fill a plane)

Yeah, and another famous example with D=2 and Dt=1 is the Hilbert curve:
http://en.wikipedia.org/wiki/Image:Hilbert_curve.png

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada