Logo by reallybigname - 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: Follow us on Twitter
Welcome, Guest. Please login or register. May 23, 2022, 03:23:08 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: Inverted MandelBulb  (Read 2624 times)
Description: Maybe there were alredy some?
0 Members and 1 Guest are viewing this topic.
Fractal Supremo
Posts: 1174

« on: December 03, 2011, 03:41:31 PM »

I' m not a shure, do someone alredy had found this. Probably did, as it is not so elaborate. Actulay, I 'm pretty new in quaternions, and I can't know all the soft. (realy I never used the most popular 3D soft) Fractal Explorer had this, but no mandelbulbs and different results, probably postprocess inversion. Blablabla...

Well, 2D fractals have post calculations transformation circle inversion. However the same results are when initialising fractal with:

z = 0;

C= recip(pixel);

When you zoom out formula still iterates area around -1 > 0 > 1, but on the inside it iterates as zoomed out > -1 ... 1 <.

Circle inverse don't work in 3D (maybe sphere inverse, but at the expense of speed.)
But quaternion formulas works pretty nicely with inverted start. C=recip(pixel); and C=1/pixel; produce different results. So recip produces fully inverted 3D "caves", much alike as in 2D. And with z=1/pixel, if not a julia set, it mostly gets inside the fractal.
Not shure about q math differences of recip and 1/x, but it looks that recip function do not inverses all of the q components. Mandelbulbs produce pretty impressive results, recip function gives something like 2D projection of mandelbulbs but in 3D terrain.

Pretty simple changes:
quaternion INV;

void init(void)
if (juliaMode)
 {         z=quaternion(partx(perturb),party(perturb),partz(perturb),0);

Here is the results,

- Mandelbulb DE, power 8, min orbit colouring, recip inverted,

- Julia mode, recip inverted, side look.

- Julia mode, 1/pixel inverted, colour speed increased by 5, calculated slower(?).

- More artsy fish like mandelbulb, 100th power, recip inverted.

- Typical recip inverted quaternion. z=conj(z^4)+c Holes in imaginary axis and swirls in the real axis.

This easyly could be implemented just as single flag in mandelbulb formulas. Even if too much changable variables and flags make formulas slow and user unfriendly.
« Last Edit: December 05, 2011, 07:03:16 PM by Asdam » Logged

fractal catalisator
« Reply #1 on: December 03, 2011, 05:24:25 PM »

Very nice. I'm sure it has been done before but I haven't. Will try it now. Thanks
Fractal Phenom
Posts: 443

« Reply #2 on: December 03, 2011, 05:43:53 PM »

Post pictures, or it didn't happen   grin
Global Moderator
Fractal Senior
Posts: 2512

Fragments of the fractal -like the tip of it

« Reply #3 on: December 04, 2011, 05:49:53 PM »

In mb3d, use this sequence

swap c-xyz
then use any formula, checking repeat from here.

I don't know why somebody must give you credit ... Inversion is one of the oldest techniques for fractals, and you can't pretend to copyright it...

No sweat, guardian of wisdom!
Fractal Supremo
Posts: 1174

« Reply #4 on: December 05, 2011, 07:02:05 PM »

Very nice. I'm sure it has been done before but I haven't. Will try it now. Thanks

It realy is pretty simple, so it suprised that mandelbulb formulas I found didn't had this feature.

Yeah, must remove credits, too simple.

cbuchner1 :
Uploader had some server problems.
« Last Edit: December 05, 2011, 07:04:54 PM by Asdam » Logged

fractal catalisator
Pages: [1]   Go Down
Jump to:  

Related Topics
Subject Started by Replies Views Last post
random.images (inverted order KIFS and a flat mbox) Images Showcase (Rate My Fractal) visual.bermarte 2 912 Last post September 29, 2010, 03:58:04 PM
by visual.bermarte
Deus ex machina of inverted worlds Mandelbulb3D Gallery KRAFTWERK 0 280 Last post November 15, 2012, 04:30:04 PM
Inverted cathedral - 3D printed fractal Mandelbulb3D Gallery bib 1 621 Last post February 03, 2013, 09:55:28 AM
by cKleinhuis
3D fractal zoom - Inverted Temple Movies Showcase (Rate My Movie) bib 0 481 Last post August 13, 2013, 12:46:52 PM
by bib
Inverted Infinities Mandelbulber Gallery mclarekin 0 407 Last post February 21, 2017, 05:23:32 AM
by mclarekin

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 0.108 seconds with 29 queries. (Pretty URLs adds 0.005s, 2q)