Originally posted by Class A Have you considered using something like the Peano curve or the Hilbert curve and use different colours for various iteration depths of the curve?

Space filling curves won't do it, I guess. You either print finite versions with a peak in frequency space or you get a uniform surface.

My current intuition uses the Cantor set as a starting point. Besides the Cantor dust (which isn't dense enough), the Sierpinski carpet is a well known generalization to 2D:

It has a Haussdorf dimension of 1.8928 and any fractal around 1.7 to 1.9 seems suitable.

List of fractals by Hausdorff dimension - Wikipedia, the free encyclopedia lists many of them in a convenient way.

However, I would alter the generation rule. Generalized Cantor sets use a rule to use a uniform plane, tile it into congruent parts, and remove

*some* of them.

I think to alter this rule: I replace a single tile center by N centers of congruent parts. Then, I "attach" a fast decaying function to the centers like a Gaussian with a standard deviation proportional to the current iteration's tile scale. For each tile center, I use a color multiplication factor where black corresponds to the removal of the subtile. Then, I overlay all tile functions with the image of the previous iteration, where the choice of the exact overlay function (e.g., a multiplication) defines much of the final fractal. The choice of Gaussians should make the power spectrum smooth.

That gives me quite some design space and I'll have to write a program to navigate thru the possibilities.

Nevertheless, I'll need hard borders to measure a camera's capability to depict line structures. The above construction only measures a camera's capability to depict point structures. So, I'll have to combine several approaches. So, a standard duochrome fractal probably won't do the job.