Logo by AGUS - Contribute your own Logo!


it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
Welcome, Guest. Please login or register. March 04, 2024, 10:37:37 AM

Login with username, password and session length

The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

Pages: [1]   Go Down
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: 3D Mandelbrot Set Phase Shift Animations  (Read 9764 times)
0 Members and 1 Guest are viewing this topic.
Posts: 122

« on: November 30, 2009, 05:45:41 PM »

Here is a way to continuously transform the negative z-component 3D Mandelbrot into the positive z-component Mandelbrot (with a rotation) by adding a phase shift:
{x,y,z}^n = r^n*{cos(phi)*cos(theta), cos(phi)*sin(theta), sin(phi)}
r=sqrt(x²+y²+z²), theta=n*atan2(y,x), phi=n*asin(z/r)+phase
where the phase varies continuously from goes from 0 to 2pi.

Here is a link showing what this animation looks like for the 8th order version:

Here is a link showing what this animation looks like for the quadratic version:

* Mandelbulb8.gif (34.62 KB, 70x70 - viewed 3776 times.)

* Mandelbulb.gif (75.09 KB, 70x70 - viewed 3690 times.)
« Last Edit: December 06, 2009, 08:47:39 PM by bugman » Logged
Fractal Phenom
Posts: 443

« Reply #1 on: November 30, 2009, 06:58:11 PM »

Very cool - I'll try and see if this is compatible with my raymarching code on the GPU. Having an animated phase in realtime would sure look nice. It might even look nice when animated veeeeerrry slowly, while the camera is deeply zoomed in.

UPDATE: Yes, I got it to work. But on my first attempt I forgot to add the phase on the part where phi is computed before entering the iterative loop. It looked distinctly different than your videos, but also very cool. It appeared more like twisting these prodtruding bulbs instead of marching the bulbs over the surface.

It seems that the initial choice of the phi phase versus the iterative choice of the phase opens a 2-dimensional parameter space for animating the fractal. As Mr. Spock would say: Highly fascinating!

How do the theta angle (in the x,y plane) effects compare to this?

I will make a new CUDA version available soon, maybe I will even open a blog for my CUDA contraptions because people had trouble getting nVidia forum accounts lately. Without such an account, the download was not possible.


« Last Edit: November 30, 2009, 11:55:17 PM by cbuchner1 » Logged
Posts: 122

« Reply #2 on: December 01, 2009, 01:38:28 AM »

Adding a phase shift to theta is not very interesting because it merely rotates the overall structure. However, I am curious to know what formula you used to get the prodtruding bulbs to twist. Do you have an animation that we can see?
Fractal Phenom
Posts: 443

« Reply #3 on: December 01, 2009, 02:08:03 AM »

Not really a formula. I've done the +phase in the iterative part of the loop only, but before entering the loop phi gets a start value that is asin(z/R). There I simply forgot to add +phase and received the effect that I described.

One could do something like the code below and choose phase1 and phase2 freely. In my accidential case described above phase1 was 0 and phase 2 was sweeped, resulting in the twisting effect. But one could also sweep phase1 from 0 to 2PI and phase2 from 2PI to 0 simultaneously. Or set phase2 = cos(t) and phase1 = sin(t) where t is being incremented. Any continuous sweep over this 2D plane would look cool. The possibilities are limitless wink

phi = asin(z/R) + phase1;
while (--iterations)
   // do your dz and z iterations, and finally update phi...
   phi = asin(z/R) + phase2;

I've already published the updated Mandelbulb version on the nVidia forums, the two phase shift animation modes are available by pressing the space bar a couple of times (it cycles through the modes).

When I get Fraps or similar video capture tools to run, I'll upload some VGA sized video to vimeo or youtube. But it will have to wait until tomorrow. It's what...  2AM now ? wink

At VGA size this renders at about 20-25 FPS on my nVidia 9600GSO (raytraced with phong shading). Adding reflections brings this down to some 7 or 8 FPS. This is a nearly 3 year old graphics card. I can only guess that a 280GTX would render this full HD (1920x1080) in real time if one can foot the power bill.
« Last Edit: December 01, 2009, 02:19:50 AM by cbuchner1 » Logged
World Renowned
Fractal Senior
Posts: 2250

use email to contact

nahee_enterprises Nahee.Enterprises NaheeEnterprise
« Reply #4 on: January 30, 2010, 08:24:06 PM »

Here is a way to continuously transform the negative z-component 3D Mandelbrot
into the positive z-component Mandelbrot (with a rotation) by adding a phase shift....

Here is a link showing what this animation looks like for the 8th order version....

I am just now getting around to viewing some of the animations I missed, and this one is rather cool the way it collapses in on (or expands out on) itself.

Pages: [1]   Go Down
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Mandelbrot Zoom Animations Fractal eXtreme Gallery Fractacular 3 1482 Last post June 25, 2013, 12:19:50 AM
by panzerboy
Please try this... new 3d mandelbrot formula, animations included Mandelbulb Implementation « 1 2 » Fred Decker 18 8925 Last post January 26, 2013, 12:42:24 AM
by Fred Decker
Classic Mandelbrot Set in 3D GIF animations Animations Showcase (Rate My short Animation) in4ur 14 3309 Last post September 12, 2014, 10:19:12 PM
by thargor6
Mandelbrot phase angle GIF loop Animations Showcase (Rate My short Animation) billtavis 4 9055 Last post February 24, 2015, 06:29:58 AM
by Chris Thomasson
Graveyard Shift Mandelbulb3D Gallery Sabine 0 1250 Last post October 18, 2016, 11:58:01 AM
by Sabine

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.13 seconds with 29 queries. (Pretty URLs adds 0.006s, 2q)