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Author Topic: True 3D mandelbrot type fractal  (Read 402107 times)
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twinbee
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« Reply #195 on: September 10, 2009, 01:51:01 PM »

Ace! I fear adding even shadowing (let alone global illumination) may choke on that!  crazy
« Last Edit: September 10, 2009, 01:59:49 PM by twinbee » Logged
cKleinhuis
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« Reply #196 on: September 10, 2009, 04:16:45 PM »

a bit moreiterations would also be nice, diffuse direct lighting is fine !

i propose, for global illumination issues, a mesh export would be better, than to include a whole global illum renderer ....
« Last Edit: September 10, 2009, 04:18:32 PM by Trifox » Logged

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David Makin
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« Reply #197 on: September 11, 2009, 10:03:37 PM »

I really must stop rendering and get on with some coding instead !

Anyway, I hope you like it:

<a href="http://www.youtube.com/v/i94NzTRCxg8&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/i94NzTRCxg8&rel=1&fs=1&hd=1</a>
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twinbee
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« Reply #198 on: September 12, 2009, 01:57:42 AM »

Cool !

How about a zoom in to 10,000x starting from 1x... (one where the camera moves in, rather than a camera type magnification (narrowing field of vision), which would only look like a 2D magnification thing, rather than an awesome 'fly through' with parallax). Naturally, the camera would need to slow down towards the end as it gets incredibly close to the object. Also, with a nice, large field of vision for maximum effect smiley
« Last Edit: September 12, 2009, 02:08:59 AM by twinbee » Logged
David Makin
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« Reply #199 on: September 12, 2009, 05:06:33 AM »

Anyone for a degree 4 Julia Set ?

http://makinmagic.deviantart.com/art/True-3D-Julia-136717735
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bugman
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« Reply #200 on: September 12, 2009, 05:31:58 AM »

Here are a couple of 3D Pickover stalks orbit traps:
http://bugman123.com/Hypercomplex/PickoverStalks-Tricorn-large.jpg
http://bugman123.com/Hypercomplex/PickoverStalks-White-large.jpg


* PickoverStalks-Tricorn.jpg (81.68 KB, 280x280 - viewed 1005 times.)

* PickoverStalks-White.jpg (90.8 KB, 280x280 - viewed 978 times.)
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bugman
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« Reply #201 on: September 12, 2009, 05:35:00 AM »

Maybe somebody made some trials with 3D Buddhabrots? I'm planning in near future to write some program for rendering 3D Buddhabrots and animations.

Here are my first attempts to create a 3D Nebulabrot (a variation of the Buddhabrot). Unfortunately, it has some bugs, but I think it will look really beautiful if I ever get the bugs ironed out:
http://bugman123.com/Hypercomplex/Nebulabrot-White.jpg
http://bugman123.com/Hypercomplex/Nebulabrot-Tricorn.jpg
« Last Edit: September 12, 2009, 06:10:18 PM by bugman » Logged
cKleinhuis
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« Reply #202 on: September 12, 2009, 04:24:50 PM »

those orbit traps variation looks beautiful !
and for the 3d buddhabrot .... you fill a 3d array with hit counter values ?! and render it as a volumetric object ?!?

 huh?
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bugman
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« Reply #203 on: September 12, 2009, 06:39:50 PM »

Here's a comparison of two different ways of calculating higher order Mandelbrot sets for Twinbee's formula. One image uses the standard method of:
{x,y,z}^8 = r^8{cos(8θ)cos(8φ),sin(8θ)cos(8φ),-sin(8φ)}

The other image uses nesting:
(({x,y,z}▓)▓)▓ where {x,y,z}▓ = r▓{cos(2θ)cos(2φ),sin(2θ)cos(2φ),-sin(2φ)}

In either case r=sqrt(x▓+y▓+z▓), θ=atan(y/x), φ=atan(z/sqrt(x▓+y▓))


* Mandelbrot-White8.jpg (59.04 KB, 280x280 - viewed 965 times.)

* Mandelbrot-White222.jpg (62.73 KB, 280x280 - viewed 978 times.)
« Last Edit: September 12, 2009, 07:51:42 PM by bugman » Logged
bugman
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« Reply #204 on: September 14, 2009, 09:31:02 PM »

those orbit traps variation looks beautiful !
and for the 3d buddhabrot .... you fill a 3d array with hit counter values ?! and render it as a volumetric object ?!?

 huh?

Yes, the 3D Buddhabrot is a volumetric rendering of a 3D array with hit counter values. I am going to try a completely different approach and see if I get better results.
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bugman
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« Reply #205 on: September 14, 2009, 09:32:09 PM »

I have improved the resolution of my 8th order version of Twinbee's Mandelbrot set:
http://bugman123.com/Hypercomplex/Mandelbrot-White8-large.jpg
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bugman
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« Reply #206 on: September 14, 2009, 09:33:22 PM »


I like this one. What constant did you use for this Julia set?
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David Makin
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« Reply #207 on: September 14, 2009, 10:58:42 PM »


I like this one. What constant did you use for this Julia set?


It's a degree 4 using your version of Twinbee's formula - i.e. the "power" version rather than the repeated squaring - and the Julia constant is (0.8,0,0).
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twinbee
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« Reply #208 on: September 14, 2009, 11:10:24 PM »

All good stuff; more zooms please! smiley

At the mo, the surface is going to be mono-hued in general (I think). I never thought we'd get to use it, but I bet Duncan's method of colouring the outside edge would produce interesting results:
http://www.fractalforums.com/mandelbrot-and-julia-set/coloring-algorithm-to-allow-for-multi-colored-mandelbrot-edge
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David Makin
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« Reply #209 on: September 14, 2009, 11:36:17 PM »

All good stuff; more zooms please! smiley

At the mo, the surface is going to be mono-hued in general (I think). I never thought we'd get to use it, but I bet Duncan's method of colouring the outside edge would produce interesting results:
http://www.fractalforums.com/mandelbrot-and-julia-set/coloring-algorithm-to-allow-for-multi-colored-mandelbrot-edge

Actually for well-behaved maths (like quats or "standard" hypercomplex) where there's an analytical distance estimator and for other fractals using the delta smooth iteration method then colouring the surface simply based on the smooth iteration value for the solid surface points should produce surface colour variation - using both methods the shape of the solid does not match the shape of the smooth iteration contours provided that the max. iteration used is large enough - in the delta case this is because "solid" is essentially based on the iteration density rather than the iteration value.
Ways of colouring the surface is something that I will include in my new set of classes when I finally get around to some more fractal coding smiley
« Last Edit: September 14, 2009, 11:38:46 PM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

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