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Fractal Math, Chaos Theory & Research => Mandelbulb Renderings => Topic started by: fractalrebel on November 30, 2009, 11:18:42 PM




Title: Ikenaga Juliabulb
Post by: fractalrebel on November 30, 2009, 11:18:42 PM
The following image is an adaption of the mandelbulb algorithm to the Ikenage Julia fractal (z^3 + (c-1)*z - c) This has been one of my favorite fractals since the early days of FractInt - early 1990's. I have added a steel mesh texture to the surface of the fractal.


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 01, 2009, 07:41:49 PM
Here is another Ikenaga Power Juliabulb image. The Julia seed is -0.0216579 + i*0.0824114 and the power is 5. I think it looks a bit like an Inca Mask.


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 01, 2009, 08:19:44 PM
Here is a colored version of Inca Mask. The pallete for the coloring actually came from some photographs of Inca ruins.


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 01, 2009, 08:23:21 PM
Arg! I realize I didn't post the formula for the Ikenaga Power Juliabulb:

z^p + (c-1)*z -c


Title: Re: Ikenaga Juliabulb
Post by: Buddhi on December 01, 2009, 10:26:45 PM
Amazing formula and great renders.
Are you using trigonometric expansion of this formula?


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 01, 2009, 10:39:33 PM
Amazing formula and great renders.
Are you using trigonometric expansion of this formula?

No, I am using the power and multiply functions described under lambdabulb.


Title: Re: Ikenaga Juliabulb
Post by: kram1032 on December 02, 2009, 12:52:02 AM
very nice fractals :D

they actually look like whipped cream varies fractally with more fractal details... if that makes sense^^


Title: Re: Ikenaga Juliabulb
Post by: cbuchner1 on December 02, 2009, 12:54:07 AM

Is the coloring scheme based on orbit trapping?

Does it simply choose the color closest to the orbit's center that is associated with a color - or does it blend between three colors?

I like the effect, maybe I should add it to my GPU raymarcher.


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 02, 2009, 02:00:00 AM

Is the coloring scheme based on orbit trapping?

Does it simply choose the color closest to the orbit's center that is associated with a color - or does it blend between three colors?

I like the effect, maybe I should add it to my GPU raymarcher.

Nope, its very simple. Color by the distance from (0,0,0) to the fractal surface.


Title: Re: Ikenaga Juliabulb
Post by: fractalrebel on December 02, 2009, 04:16:45 AM
Nope, its very simple. Color by the distance from (0,0,0) to the fractal surface.

I should pay attention to my own code. the coloring is based upon the distance to the camera.


Title: Re: Ikenaga Juliabulb
Post by: subblue on December 19, 2009, 11:59:11 PM
I've added your formula to my Pixel Bender script and with some other additions to add alternating Julia seeds I'm finding some interesting structures :)

(http://farm3.static.flickr.com/2525/4197910173_6d46e4ca26_b.jpg)


Title: Re: Ikenaga Juliabulb
Post by: kram1032 on December 20, 2009, 01:16:45 AM
Wow, now that's nice :D
A very organic shape :)

Is this at low iteration count or will it stay that smooth?


Title: Re: Ikenaga Juliabulb
Post by: subblue on December 20, 2009, 10:07:19 AM
Is this at low iteration count or will it stay that smooth?
Thanks. The iteration count was very low, about 3 or 4. Increasing it added fine details in the mid section that distracted from the overall shape.


Title: Re: Ikenaga Juliabulb
Post by: kram1032 on December 20, 2009, 03:00:17 PM
At this level it looks like the mix of an alien mothership (with some UFOs around it) and an alien garden :D