Buddhabrot R&D Gallery

[richardrosenman]

I've been doing quite a bit of testing on my Buddhabrot generator with new and unique techniques and I figured this would be a good place to post them.

This first image stemmed from this thread in which cbuchner1 shows is fantastic Buddhabrot spectral renders! http://www.fractalforums.com/images-showcase-(rate-my-fractal)/buddhabrot-reinvented/

I experimented with such a technique but ran into some roadblocks, particularly in the way that my plugin is coded versus his would require quite an overhaul for a similar treatment. However, that led me into trying out HSV spectral coloring techniques and the results turned out nicely. Basically, this involves coloring the Buddhabrot by mapping the orbit length to the Hue channel of HSV color space. As the orbit length increases, the color hue changes therefore using the entire color spectrum to color with. This, in turn, reveals many Buddhabrot features that were previously difficult to see:


  
Most of these images have had levels adjusted for optimal presentation.

-Richard

[richardrosenman]

Having had good results with the HSV, I tried Lab color space:



Of course, it all depends on what channel you map it to. In this case, the coloring was mapped to the 'b' color-opponent dimension but it could have been mapped to the 'a', although it didn't yield as nice results. You could also map to both and change the balance between the two for even more unique effects. The 'L' channel in Lab simply controls lightness so it would simply produce somewhat boring luminance-based renders.

-Richard

[richardrosenman]

And another interesting test, this one using the IUV color space and mapped to the 'V' channel (I believe):



-Richard

[kram1032]

If you convert Lab to HSL (just L, radius from whitepoint and relative angle to whitepoint) does that look any different to the HSV one?

[richardrosenman]

If you convert Lab to HSL (just L, radius from whitepoint and relative angle to whitepoint) does that look any different to the HSV one?

Hi Kram1032;

I'm not sure which L you mean (the Lab or HSL) and which component you want to map to... Here's some pseudo code of my process. Maybe you can re-write it to show me what you mean and I'll give it a shot.


h = rgb2hsl (red ,green,blue,0);
s = rgb2hsl (red ,green,blue,1);
l = rgb2hsl (red ,green,blue,2);

pset(x,y,0,hsl2rgb(red,s,l,0));
pset(x,y,1,hsl2rgb(green,s,l,1));
pset(x,y,2,hsl2rgb(blue,s,l,2));

[kram1032]

H = atan2(Lab.b,Lab.a)
S = sqrt(Lab.a²+Lab.b²)
L =  Lab.L

And use those just in the way, you used HSV before.
I hope, that's clear

[richardrosenman]

Hi Kram1032;

Well, here's what I get using this method:



There's definitely some problems with this because it doesn't work in 16 bit mode, only 8. In addition, after some further investigation, here's what I found:


depth=255.0;
red = red*depth;
green = green*depth;
blue = blue*depth;
l = rgb2lab ((int)red ,(int)green,(int)blue,0);
a = rgb2lab ((int)red ,(int)green,(int)blue,1);
b = rgb2lab ((int)red ,(int)green,(int)blue,2);


h = (int)atan2((float)b,(float)a);
s = (int)sqrt((float)a*(float)a+(float)b*(float)b);
l2 = l;


Above, h always returns one which is most likely a problem.


pset((int)x,(int)y,0,hsl2rgb(h,s,l2,0));
pset((int)x,(int)y,1,hsl2rgb(h,s,l2,1));
pset((int)x,(int)y,2,hsl2rgb(h,s,l2,2));


Is this the algorithm you had in mind? I have a feeling there's a flaw in here somewhere...

-Richard

[richardrosenman]

On another note, neat result of the Tricorn using HSL color space mapping:



-Richard

[lycium]

very interesting buddhabrots on display here, you're all making me want to render some of my own *jealous* 

great work!

[cKleinhuis]

buddhabrots offer nice views of well known formulas, i would love to see more formulas rendered as buddhabrots ( hybrid formulas, any other existing fractal )
and also i would be interested in a 3d version of the buddhabrots made of triplex numbers

[kram1032]

the H value always returns 1? That definitely should NOT happen....

atan2(y,x) should give the angle (x,0,y) in radians, so the angle that points from the origin to the point in the plane.
As the Lab space is built in this way, it should work perfectly...

Well, allthough it's only red, it looks very nice
And the tricorn of it looks great

[richardrosenman]

the H value always returns 1? That definitely should NOT happen....

atan2(y,x) should give the angle (x,0,y) in radians, so the angle that points from the origin to the point in the plane.

I took a quick look at it tonight and noticed that the result of atan2(b,a) spits out a float between 0 and 1. Since I was converting to integer, it rounded it off to one. For this test, I multiplied that float by the color bit depth and then converted to int. Here's the result:



It's a bit better but not really to my liking. At least you see a lot more detail than the previous one!

-Richard

[richardrosenman]

I let this test go last night and it turned out quite nice. Heading describes the technique:



-Richard

[kram1032]

you multiplied by the colour bit depth?
I think, that's wrong but I'm not sure...

Why not use the float and convert to ints later?
Also the atan2 function in theory should return values from 0 to 2pi or from -pi tp pi...
Oh well, maybe the definition is different for some unknown reason...


The split comples Buddhabrot looks beautiful
The heading?

[richardrosenman]

I did some tests a while back based on Ker2x's interesting Buddhabrot mutations that can be found here:

http://www.fractalforums.com/fractal-programs/a-creative-buddhabrot-rendering/

This first test involves computing a random c-point, and then incrementing xa or ya by 0.0001. Once you reach a million samples, you recompute a new random c-point and do it all over again. By incrementing xa / ya, you produce lines instead of points:



Of course, the problem with this is that the longer you let it iterate, the more it will develop to look like a typical Buddhabrot render so unlike the standard practice, the less time you iterate, the more unique it looks. Iteration time here was only 20 minutes.

-Richard