Smokin'

[Fractal Ken]

Generated by homemade software with minor post-processing in GIMP.

[Kali]

This is excelent Ken! did you use exponential smoothing for coloring?

[Fractal Ken]

Thanks, Kali. I'm not sure what exponential smoothing is. (I don't understand most of the coloring terminology people use.) What I did is a little complicated. I used 4 slightly different coloring methods on this fractal; they're probably considered orbit traps.

[Kali]

I asked because I get much the same aethereal look with some fractals by using that method, wich I know from Ultrafractal but it's in fact this.

Take a look at this image, I used exponential smoothing for coloring the fractional part only of the modulus in the formula z=1/(z*z+c):



Now it's my favorite coloring method, all of my last 2D fractals uses it, and will be the main used in the fractal program I'm writing because it works very nice with the hybrids I'm doing. But is not the same as Ultrafractal's because I'm not using the complex Z, just the modulus. You have to add this into the iteration loop: sum=sum+exp(-1/abs(NewModulus-OldModulus)), then color using the resulting value of "sum".

[Fractal Ken]

Kali, your picture has a beautiful glow. Thanks for the information on exponential smoothing. I recall the term from time series analysis, but I hadn't connected it with fractal coloring.