Title: Juliabulbs by bending Post by: msltoe on October 01, 2013, 03:20:03 AM I've lost count on the number of hours of sleep I've lost over the years looking for the Holy Grail. I know it's technically not possible, but I always wanted to be able to fuse multiple Juliabulbs together. In the past, I've managed to yz symmetrize a specific Julia set that basically behaves a lot like the burning ship. But I've never been able to symmetrize a z^2 Julia set (where b is non-zero) ... until now. As I was lying awake last night, I realized that if I bent the juliabulbs, I could match up the right polarities so I don't get the mismatched edges. I don't have a perfect bending function yet, and only Julia sets look OK so far, but here's an inner loop code that people can try out:
if (z>0) {d = 1;z=z;} else { d = -1;z=z; } z = fabs(z); r=sqrt(z*z+y*y); z1 = (z*z-y*y)*r; y1 = (2*y*z)*r; z = z1+z; y = y1+y; z = (z)*d; r = x*x+y*y+z*z; x1=(x*x-y*y)*(1-z*z/r); y1=(2*x*y)*(1-z*z/r); z1=-2*z*sqrt(x*x+y*y+0.25*z*z); x = x1+a; y = y1+b; z = z1+c; iter++; And here's a picture of [-0.8,-0.1,0]: (http://nocache-nocookies.digitalgott.com/gallery/14/803_01_10_13_3_11_42.png) Title: Re: Juliabulbs by bending Post by: KRAFTWERK on October 01, 2013, 08:30:49 AM Woahhhh! O0
I will not say I am happy you are sleepless msltoe but... I love that julia! Excited to see what more lies hidden in your "bent brot"! :beer: Title: Re: Juliabulbs by bending Post by: msltoe on October 01, 2013, 02:09:22 PM I see some promise in this approach, but I will need new bending functions to be able to handle other seed regions. A universally-applicable bending function could lead to a good M-set.
Title: Re: Juliabulbs by bending Post by: Nahee_Enterprises on October 01, 2013, 04:15:05 PM I've lost count on the number of hours of sleep I've lost over the years looking for the Holy Grail. I know it's technically not possible, but I always wanted to be able to fuse multiple Juliabulbs together. In the past, I've managed to yz symmetrize a specific Julia set that basically behaves a lot like the burning ship. But I've never been able to symmetrize a z^2 Julia set (where b is non-zero) ... until now. As I was lying awake last night, I realized that if I bent the juliabulbs, I could match up the right polarities so I don't get the mismatched edges. I don't have a perfect bending function yet, and only Julia sets look OK so far, but here's an inner loop code that people can try out: ........... And here's a picture of [-0.8,-0.1,0]: http://nocache-nocookies.digitalgott.com/gallery/14/803_01_10_13_3_11_42.png (http://nocache-nocookies.digitalgott.com/gallery/14/803_01_10_13_3_11_42.png) I see some promise in this approach, but I will need new bending functions to be able to handle other seed regions. A universally-applicable bending function could lead to a good M-set. Very cool !!! :toast: With all the bending going on, I am not sure whether to refer to these as the "Kama Sutra" or "Yoga" series of fractals. Definitely some contortionist techniques involved. :D Title: Re: Juliabulbs by bending Post by: Alef on October 01, 2013, 05:41:33 PM Not bad, certain grailishness in it. Maybe two variable equations could give something. Quote I know it's technically not possible, Rucker bulb seems to be closest to it. |