Wrote a little OpenCL thing to compute multifractal spectrum. Fed it with the histogram (exported from a patched version of Fractorium) from a fractal flame by C-91 (the colours here are slightly different, I experimented with auto-white-balance post-processing stuff).

Another multifractal spectrum of the same fractal flame as before. This time it's f(alpha) vs alpha instead of D(Q) vs Q.

A cluster of lines start near (1.5, 1.4) and get closer to each other as they increase (progressively more slowly) towards (2,2).

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Better multifractal spectrum graphs for the fractal flame upthread. The main difference is that the Q range is higher, and more of it is calculated in OpenCL.

Still need to move the simple linear regression code into OpenCL and get it working on GPU (the OpenCL works perfectly fine on CPU, but on my GPU it outputs garbage (different on each run) - even the initial image mipmap reduction stage fails).

Computation time with 1024 Q steps is 23mins on CPU, input histogram image resolution 7280x7552x4 f32.

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Added EXR import to my calculator. Hacked an option into command line renderer to output raw histogram data to EXR. Ran a batch process to render and analyze some of the examples that come with Fractorium (in its Data/Bench directory).


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> "Direct determination of the f(α) singularity spectrum" Ashvin Chhabra and Roderick V. Jensen Phys. Rev. Lett. 62, 1327 – Published 20 March 1989

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The f(q) vs a(q) curves look a bit crisper with this method.

And calculating D(q) is easy, just
$$D = (a * Q - f) / (Q - 1)$$

I ported the linear regression to OpenCL too, now only input and output needs to run on the CPU, GPU does all the calculations.

Some of the test histograms I'm using give bizarro curves though, not sure what's up - bizarro with two different algorithms means it's probably (?) a real behaviour?

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@mathr Nice to see a graph gently gliding down toward asymptote these days.

@KnowPresent the other graph I just posted is increasing, but at least it curves downwards a bit...

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