• July 24, 2021, 04:46:59 PM

### Author Topic: (Question) Is this what a histogram coloring of the Mandelbrot set should look like?  (Read 1477 times)

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#### claude

• Posts: 1937
##### (Question)Re: Is this what a histogram coloring of the Mandelbrot set should look like?
« Reply #15 on: July 02, 2019, 09:34:06 AM »
Oh! Ok, I see what you did.  That should be much fast but quality may suffer if the bin spacing isn't fine enough.  It's also heavily dependent on the minimum and maximum iteration counts achieved in the image because the bins are equally spaced.

More detail on my method:
O(W * H * N) for calculating the iteration counts, where N is the average iteration count per pixels.
O(B * log(B)) for sorting the histogram with B  = W * H unevenly spaced bins (one bin per pixel).
O(W * H * log(B)) for looking up the histogram per pixel.

Maybe it's possible to do a hybrid, subsampling the image to reduce B to more sensible levels (because 10-bit accuracy in the final image is perfectly fine for most purposes). Would need a custom bsearch() that returns a neighbour of the element's position if the element is not found (instead of NULL which is absolutely useless).

#### Duncan C

• Fractal Friend
• Posts: 14
##### Re: Is this what a histogram coloring of the Mandelbrot set should look like?
« Reply #16 on: August 23, 2019, 04:08:01 AM »
I think the problem you may be facing is where you place the transition from the black-to-blue color gradient and the blue-to-white gradient. I implemented histogram-based colors in my app, Fractalworks.

When I manually set that transition at 17 iterations in FractalWorks to plot using histogram-based color gradients and integer iteration values I get a plot that I think looks better than your linear color table plot:

FractalWorks also lets you use histogram information to decide where to place color transitions. When I switch to histogram-calculated transitions and make the transition from the black-to-blue gradient to the blue-to-white gradient at the point where 95% of pixels are plotted with the black-to-blue gradient, the result looks nearly identical, but now the colors assignments are adaptive (which is a major benefit of histogram-based color schemes.)
« Last Edit: August 24, 2019, 01:28:09 AM by Duncan C »

#### Duncan C

• Fractal Friend
• Posts: 14
##### Re: Is this what a histogram coloring of the Mandelbrot set should look like?
« Reply #17 on: August 24, 2019, 01:35:13 AM »
With histogram-based colors a simple one-gradient color scheme produces nice looking colors and decent definition of the shapes for pretty much any plot.

Here is a plot of Map 48 from the Beauty of Fractals using a simple blue-to-white histogram based gradient:

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