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
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada