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 Author Topic: Ikenaga Juliabulb  (Read 3531 times) Description: 0 Members and 1 Guest are viewing this topic.
fractalrebel
Fractal Lover

Posts: 211

 « 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.
 Twisted2.jpg (191.01 KB, 900x720 - viewed 560 times.) Logged

fractalrebel
Fractal Lover

Posts: 211

 « Reply #1 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.
 IncaMask.jpg (106.68 KB, 640x640 - viewed 575 times.) Logged

fractalrebel
Fractal Lover

Posts: 211

 « Reply #2 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.
 IncaMask_Color.jpg (215.65 KB, 900x900 - viewed 566 times.) Logged

fractalrebel
Fractal Lover

Posts: 211

 « Reply #3 on: December 01, 2009, 08:23:21 PM »

Arg! I realize I didn't post the formula for the Ikenaga Power Juliabulb:

$z^p + (c-1)*z -c$
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Buddhi
Fractal Iambus

Posts: 895

 « Reply #4 on: December 01, 2009, 10:26:45 PM »

Amazing formula and great renders.
Are you using trigonometric expansion of this formula?
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fractalrebel
Fractal Lover

Posts: 211

 « Reply #5 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.
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kram1032
Fractal Senior

Posts: 1863

 « Reply #6 on: December 02, 2009, 12:52:02 AM »

very nice fractals

they actually look like whipped cream varies fractally with more fractal details... if that makes sense^^
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cbuchner1
Fractal Phenom

Posts: 443

 « Reply #7 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.
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fractalrebel
Fractal Lover

Posts: 211

 « Reply #8 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.
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fractalrebel
Fractal Lover

Posts: 211

 « Reply #9 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.
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subblue
Conqueror

Posts: 116

 « Reply #10 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

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www.subblue.com - a blog exploring mathematical and generative graphics
kram1032
Fractal Senior

Posts: 1863

 « Reply #11 on: December 20, 2009, 01:16:45 AM »

Wow, now that's nice
A very organic shape

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

Posts: 116

 « Reply #12 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.
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www.subblue.com - a blog exploring mathematical and generative graphics
kram1032
Fractal Senior

Posts: 1863

 « Reply #13 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
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