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Author Topic: Higher Iterations  (Read 11310 times)
Description: How the interior of a minibulb is filled on higher iterations.
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trafassel
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trafassel
« on: January 15, 2010, 11:02:14 PM »

Here is an picture from the border of the spine with 17 Iterations.


* Data56pic10002_17Iterations.jpg (127.42 KB, 1280x720 - viewed 595 times.)
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trafassel
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trafassel
« Reply #1 on: January 15, 2010, 11:03:48 PM »

The same area with 18 iterations.


* Data56pic10003_18Iterations.jpg (129.5 KB, 1280x720 - viewed 565 times.)
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trafassel
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trafassel
« Reply #2 on: January 15, 2010, 11:05:09 PM »

... and with 19 iterations.


* Data56pic10004_19Iterations.jpg (133.07 KB, 1280x720 - viewed 571 times.)
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trafassel
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trafassel
« Reply #3 on: January 15, 2010, 11:07:41 PM »

It looks like the inner part of this area ist filled with the outer part of the mandelbulb stuff.

20 Iterations:


* Data56pic10005_20Iterations.jpg (138.27 KB, 1280x720 - viewed 544 times.)
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trafassel
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trafassel
« Reply #4 on: January 15, 2010, 11:10:27 PM »

The stange thing ist, that some areas seems to be not changing, only the cream stuff...

(21 iterations).


* Data56pic10006_21Iterations.jpg (143.54 KB, 1280x720 - viewed 525 times.)
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trafassel
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trafassel
« Reply #5 on: January 15, 2010, 11:13:53 PM »

This strange cream does not appear on the 2d mandelbrot set ...

(22 Iterations).



* Data56pic10007_22Iterations.jpg (153.43 KB, 1280x720 - viewed 560 times.)
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trafassel
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trafassel
« Reply #6 on: January 15, 2010, 11:29:47 PM »

... but on higher iterations, you get a sort of spiral ... like the 2d mandelbrot spiral.

(27 Iterations)


* Data56pic10012_27Iterations.jpg (177.13 KB, 1280x720 - viewed 639 times.)
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cKleinhuis
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« Reply #7 on: January 15, 2010, 11:44:29 PM »

nice sequence, feel free to post deeper depths!

great sequence, love it how more and more details evolve !

 Repeating Zooming Self-Silimilar Thumb Up, by Craig
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divide and conquer - iterate and rule - chaos is No random!
trafassel
Fractal Bachius
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trafassel
« Reply #8 on: January 16, 2010, 09:27:44 AM »

... and with 50 iterations, the inner part of the mandelbulb becomes more chaotic (at least in my renderer Gestaltlupe).



* Data57pic10003_50iterations.jpg (149.29 KB, 1280x720 - viewed 607 times.)
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kram1032
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« Reply #9 on: January 16, 2010, 07:05:36 PM »

Nice sequence smiley

I guess, that "chaotic behaviour" is the next generation of dentrites?

The set's area (volume, respectively) grows smaller and smaller to the limiting shape, rahter than bigger and bigger after all...
So, it should be like an additional fold of a new series of shapes smiley
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trafassel
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trafassel
« Reply #10 on: January 17, 2010, 06:39:36 PM »

First test for a rendering with 9000 Iterations. In the next week (if my animation sequence is ready) i will start the final rendering. 





* Data57pic10008b.jpg (128.51 KB, 1280x720 - viewed 572 times.)
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twinbee
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« Reply #11 on: January 17, 2010, 07:48:49 PM »

Nice shots! It would seem that higher iterations add more 'whipped cream' in general (at least covering the detail). I did something like this a while ago too - may as well put it all together. The numbers represent the iteration level. Look at iteration 15-17, there's a whole tier created above the previous layers. You could go inside....









Here's a higher res of one of them:
« Last Edit: January 17, 2010, 08:00:51 PM by twinbee » Logged
kram1032
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« Reply #12 on: January 17, 2010, 08:08:58 PM »

twinbee: just wondering, wether an overlay of all of them together would allow both hidden and later comming details... smiley

Maybe, a glow-ish buddhabrot variant (or in general a transparent one) could help with the look. (You would have to compromise between clearness and transparency, maybe by doing a distance estimation based transparency level from the inside: The closer to the outer edge, the either more or less transparent, depending on wether you look from the inside or the outside smiley )
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miner49er
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« Reply #13 on: January 18, 2010, 01:29:03 PM »

Wow, love your iteration sequence twinbee!

I would love to have a look 'inside' to see how the obscured areas develop with higher iterations.

Although, I would love to develop my own ray tracer, I don't have the time right now - what's the simplest/quickest way of setting up a renderer for the mandelbulb? For linux...

cheers, and keep the incredible images coming!
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trafassel
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trafassel
« Reply #14 on: January 18, 2010, 04:15:37 PM »

Very great pictures. This 'whipped cream' is for me at this time the most interesting part in the mandelbulb theory.

I want to know, if this iteration steps convergence (it must, because ther is only limited space in the mandelbulb). The problem is, that higher iterations needs (especially for the inner part) very much CPU-time.   

I think its time for some theoretical research.

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