HPDZ
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« on: January 05, 2009, 11:53:17 PM » |
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I've written a short comparison of the rank-ordering and histogram methods (and some other typical ones) of mapping counts to colors http://www.hpdz.net/TechInfo_Colorizing.htm. I made some test images and graphs showing the effect of each method on some different images. I call them "non-parametric" because they are not based on any analytic model of how the counts are distributed (e.g. linear, log); a similar name is used for statistical tests that do not assume how the data is distributed. This is a follow-up to a conversation between Duncan C and me in a different thread. Continuing to go into more detail on this issue in that thread seemed to off-topic, so I am starting a new one here. |
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Duncan C
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« Reply #1 on: August 27, 2009, 03:01:02 AM » |
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HPDZ,
I only now found this post. Excellent article. Thanks for taking the time to write it.
Duncan C
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Regards,
Duncan C
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HPDZ
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« Reply #2 on: September 21, 2009, 11:08:54 PM » |
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Duncan,
I just now found your reply. Glad you liked my article. Thanks for taking the time to read it.
Mike
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johandebock
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« Reply #3 on: February 11, 2010, 02:10:15 PM » |
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Thanks for the valuable info! I implemented the Rank-Order Mapping mapping method in my Buddhabrot renderer from start. Now I also included the Histogram Mapping. Histogram Mapping produces much more detail in some images: Rank-Order Mapping:  Histogram Mapping:  |
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KRAFTWERK
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« Reply #4 on: February 11, 2010, 03:36:02 PM » |
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Beautiful renders!  |
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Tglad
Fractal Molossus
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« Reply #5 on: February 12, 2010, 01:41:23 AM » |
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Nice write up, it seems to be missing two points.
Firstly, what about when you want to zoom in on a fractal? With histogram or rank order mappings the colour for any point on the set will change as you zoom, which most people wouldn't want.
Secondly, it doesn't seem to consider repeating the palette as a solution. If you use a log measure on the count and repeat the palette then the image will hardly vary when you change the max iterations, and the colouring will stay the same when you zoom in and out.
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reesej2
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« Reply #6 on: March 21, 2010, 05:02:19 AM » |
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The color certainly does change as you zoom, which is a problem if you're progressing through the Mandelbrot set, trying to find an interesting spot. I've tried this color method myself and it's VERY nice, but I'd advise just using it to highlight details once you've found a spot you like. The problem with using a log measure is that, while it is possible to get an even distribution with that method, it requires fine-tuning the parameters for every image. Otherwise, certain sections end up flat and plain, while others are so chaotic they're just static.
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Botond Kósa
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« Reply #7 on: April 14, 2010, 09:40:38 PM » |
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Hi Mike,
I've read your article on hpdz.net, and based on that idea I implemented rank-order mapping in my own Mandelbrot generator. I found that even rank-order mapping washes out the fine detail near the edges of the set. However, this can be corrected by transforming the output of the mapping (the [0,1] interval) with a function that also maps into [0,1], but has a higher differential at values near 1.
The first attached example shows a minibrot with standard rank-order coloring. On the second image I transformed the mapping with the function 1-sqrt(1-u). Using cube root or fourth root can increase the effect even further.
Botond
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reesej2
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« Reply #8 on: April 15, 2010, 12:27:25 AM » |
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Oh, interesting idea... it makes sense that rank-order wouldn't be the final word on the subject... I wonder if logarithms would help here, too. I've found that anywhere roots help, a logarithm helps even more.
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kram1032
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« Reply #9 on: April 15, 2010, 12:40:42 AM » |
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getting best out of all worlds  |
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Timeroot
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« Reply #10 on: April 15, 2010, 01:28:46 AM » |
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One way to do it with logarithms would be with the function 1 + 1/(log(1-x)-1). This will still map [0,1] to [0,1] monotonically increasing, also with infinite derivative at x=1.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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ker2x
Fractal Molossus
Posts: 795
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« Reply #11 on: September 27, 2010, 11:53:34 PM » |
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anyone have a mirror ? the website is down  |
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blob
Strange Attractor
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« Reply #12 on: September 28, 2010, 12:26:46 AM » |
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Does not seem to be down from here. Try again.
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ker2x
Fractal Molossus
Posts: 795
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« Reply #13 on: September 28, 2010, 09:15:36 AM » |
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Does not seem to be down from here. Try again.
indeed, it's back for me too. thank you |
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Sigillum Militum
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« Reply #14 on: April 03, 2012, 04:25:27 PM » |
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I'm glad you posted that. It's great to have such smart people here.
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