Title: Mandelbulb Variant Post by: Kali on February 08, 2012, 11:09:51 PM I just got this mandelbulb variation by modifying Fragmentarium's formula.
Instead of converting to polar, multiplying both angles and then converting back to cartesian, I did it in two parts: get polar, first multiply theta, convert back to cartesian and then the same with the resulting phi. To see it, just replace pow function with this: Code: void powN1(inout vec3 z, float r, inout float dr) {Maybe it could be optimized, I just made it in an easy and intuitive way. Some images of pow 2: Title: Re: Mandelbulb Variant Post by: DarkBeam on February 08, 2012, 11:31:46 PM Pablo please paste the whole frag script, so we can do some tests :)
Looks a lot like Xenodream variant. Julias should be great, but too many functions slow down a lot. to optimize you need a Mathematica cd or wolfram alpha... :) Title: Re: Mandelbulb Variant Post by: Kali on February 09, 2012, 12:18:01 AM Pablo please paste the whole frag script, so we can do some tests :) Looks a lot like Xenodream variant. Julias should be great, but too many functions slow down a lot. to optimize you need a Mathematica cd or wolfram alpha... :) Ok. Title: Re: Mandelbulb Variant Post by: cKleinhuis on February 09, 2012, 12:21:52 AM but the method you described would not lead to new results, because converting it back to cartesian and then again to polar, hmm, there might be going on some folding because of those hairy balls ? think so ... i mean it lies in the angles, have you a number example for what the ( between ) results are with and without your method ?
Title: Re: Mandelbulb Variant Post by: cKleinhuis on February 09, 2012, 12:28:02 AM thx for posting the frag, interesting, it is a normal power8 bulb and a somehow flattened out mandelbrot, isnt it interesting that just in the lower powers new shapes emerge ?
and the power 8 is lookin just normal Title: Re: Mandelbulb Variant Post by: visual.bermarte on February 09, 2012, 12:35:30 AM Try changing z inside powN2 ;D
z = abs(zr*vec3( cos(zo)*cos(zi), cos(zo)*sin(zi), sin(zo) )) or just add z=abs(z) after z = zr*vec3( cos(zo)*cos(zi), cos(zo)*sin(zi), sin(zo) ) Code: #preset julia1 absbulb (http://fc03.deviantart.net/fs70/i/2012/039/6/c/absbulb_by_bermarte-d4p3e2n.jpg) I just realized that I hijacked this thread! Sorry everyone! :embarrass: Title: Re: Mandelbulb Variant Post by: Kali on February 09, 2012, 09:16:15 AM Quote but the method you described would not lead to new results, because converting it back to cartesian and then again to polar, hmm, there might be going on some folding because of those hairy balls ? think so ... i mean it lies in the angles, have you a number example for what the ( between ) results are with and without your method ? Yeah, at first I thought the same, but honestly I don't know what's going on, just tried and got this ;D Quote thx for posting the frag, interesting, it is a normal power8 bulb and a somehow flattened out mandelbrot, isnt it interesting that just in the lower powers new shapes emerge ? and the power 8 is lookin just normal It's not a normal power 8 I think, but yes, it has more unique features on the lower powers. Quote I just realized that I hijacked this thread! Sorry everyone! Don't worry, that absbulb is very interesting too :) Title: Re: Mandelbulb Variant Post by: Kali on February 09, 2012, 11:38:15 PM but the method you described would not lead to new results, because converting it back to cartesian and then again to polar, hmm, there might be going on some folding because of those hairy balls ? think so ... i mean it lies in the angles, have you a number example for what the ( between ) results are with and without your method ? If I'm not wrong, when changing theta and then getting the new coordinates, phi is affected and this is why the result is different. I also have another ideas for trying, but I hadn't do the math, just a visualization of the transforms... I need to review some more trigonometry in order to achieve it :banginghead: Title: Re: Mandelbulb Variant Post by: DarkBeam on February 09, 2012, 11:44:57 PM no need to review, just type it in wolframalpha
example try simplify(sin(2*atan(y/x)) only be careful some funcs are not expanded correctly Title: Re: Mandelbulb Variant Post by: Kali on February 21, 2012, 03:05:29 PM Another way of getting some weird but interesting results, is using different scaling factors for both angles and the radius. It also works better with lower powers. In the following image is a pow 2 mandelbulb with one of the angles multiplied by 4 and the other by 3 (power x 2, and power x 1.5). Also the radius is scaled by half.
(http://img214.imageshack.us/img214/6139/mandelbulb3.jpg) I attached the Fragmentarium file. AF1, AF2, and RF parameters are the scaling factors. Title: Re: Mandelbulb Variant Post by: Kali on February 21, 2012, 04:16:59 PM Another example...
(http://img36.imageshack.us/img36/8058/kbulb1.jpg) Title: Re: Mandelbulb Variant Post by: KRAFTWERK on February 21, 2012, 04:33:43 PM All these images looks very interesting Kali!
Following this thread from now on. O0 Title: Re: Mandelbulb Variant Post by: M Benesi on February 25, 2012, 10:23:17 PM Some of those look like my old power2 formula that constrains signs in specific ways. https://picasaweb.google.com/103496528720991269557/NewComparisonShots# (was new many moons ago) Was actually thinking of letting Jesse and Darkbeam know about the cosine specific function that can be used to modify specific REAL portion of cosine signs (signs as in +/-) in fractals without resulting in discontinuity. Used it in a couple old formulas (mag vs. xyz and "3d mandelbrot attempt")... anyways. Edited to add this image of a 1,1,1 Julia of that type. Nothing great, click on image to enlarge if you want. (https://lh5.googleusercontent.com/-E9Jz7H0ZjZQ/T0sDRRbEK3I/AAAAAAAABWg/dny-0GCjycA/s640/where%2520to%2520put%2520this%2520julia.jpg) (https://lh5.googleusercontent.com/-E9Jz7H0ZjZQ/T0sDRRbEK3I/AAAAAAAABWg/dny-0GCjycA/s0/where%2520to%2520put%2520this%2520julia.jpg) |