Title: Another 3-D mandelbrot attempt Post by: msltoe on January 08, 2013, 03:53:14 AM Figure out what I'm trying to do here. I'll explain later...
First part: r = x*x+y*y+z*z; r1 = sqrt(r); phi = asin(z/r1); r2 = 1.0/sqrt(fabs(cos(phi))); if (r2>10){x=1000;} else { // Don't bother at phi near pi/2. phi = r2 * phi; r1 = pow(r,0.5*r2*r2); r3 = sqrt(x*x+y*y); x1 = r1*x/r3*cos(phi); y1 = r1*y/r3*cos(phi); z1 = r1*sin(phi); x=x1;y=y1;z=z1; Second part: x1 = (x*x-y*y); y1 = (2*x*y); z1 = 2*z*sqrt(x*x+y*y+z*z); x = x1+a; y = y1+b; z = z1+c; } Also, I transform a,b,c at the start using a similar transform as the first part. Here's the M-set: Title: Re: Another 3-D mandelbrot attempt Post by: msltoe on January 08, 2013, 04:02:09 AM A J-set at (0, -0.65, 0):
Title: Re: Another 3-D mandelbrot attempt Post by: Alef on January 08, 2013, 08:09:51 AM It reminded me of chameleon eyes:
(http://youngagropreneur.files.wordpress.com/2011/10/chameleon-1.jpg) A Mandelchameleon;) Could you make larger powers. Power 3 shape in 3D somewhat reminds two headed turtle, maybe power 3 simmetry fitts better a 3D. Title: Re: Another 3-D mandelbrot attempt Post by: kram1032 on January 08, 2013, 08:56:08 AM very interesting. Instead of whipped cream, we get what looks like "perfect" smoothness.
Certainly nice. Title: Re: Another 3-D mandelbrot attempt Post by: msltoe on January 08, 2013, 05:22:32 PM kram1032: I like your analysis.
Alef: pretty pic. What's the formula? ;) What I think is missing is a little more density of the bulb parts. I've tried a few tricks like reflections in phi space, but nothing appears as clean as the original. Title: Re: Another 3-D mandelbrot attempt Post by: jehovajah on January 11, 2013, 03:49:42 AM Very nice and what i felt you would be able to do! A little texture in the colouring algorithm maybe, but who can get any closer to the spherical trochoids? May be Matt might have an idea or two! :star: |