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Author Topic: Mandelbrot cross 2D version of Mandelbox?  (Read 2336 times)
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twinbee
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« on: October 20, 2010, 02:50:03 PM »

As we know, there are some great results if we cross the Mandelbulb with the Mandelbox (the result is sometimes called the 'BulbBox').

Perhaps it's been thought of already, but why not cross the 2D version of the Mandelbox with the traditional Mandelbrot? We should in theory see some stunning new patterns as both sets have great detail.
« Last Edit: October 20, 2010, 02:51:37 PM by twinbee » Logged
jwm-art
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« Reply #1 on: November 23, 2010, 12:10:30 AM »

Ok I've given it a go. The 2D mandelbox is not as amazing as it's 3D counterpart, nor as interesting as the Mandelbrot set itself. I've played around with a hybrid of the two and found some interesting results.


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4360


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4359
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bib
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« Reply #2 on: November 23, 2010, 12:18:56 AM »

I like the second one a lot. What do you call "cross" exactly?  I have always wondered what is being the so-called Bulbox in M3D.

Btw, the Mandelbox in 2D can give very interesting results. One of my favorite is this one I did a long time ago in UF with David Makin's formula:


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1431

<a href="http://www.youtube.com/v/YRSLJE2F_JA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/YRSLJE2F_JA&rel=1&fs=1&hd=1</a>
« Last Edit: November 23, 2010, 12:30:24 AM by bib » Logged

Between order and disorder reigns a delicious moment. (Paul ValÚry)
jwm-art
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« Reply #3 on: November 23, 2010, 02:25:27 AM »

I remember seeing that image but I had assumed it was looking flat on at a 3D Mandelbox - it does appear to have 3 dimensionality - and a light source... And it does look like it has more in common with the 3D Mandelbox than (at least my efforts at) 2D Mandelboxes. For instance in Mandelbulber (with which I only have a passing familiarity with) until you hit 'render 3d' you get a 2d version - but as a slice through a 3d fractal.

The images I posted above are purely 2D fractals - no slicing! The formula I'm using here (in a pseudo-pseudo code):

http://www.fractalforums.com/programming/understanding-the-mandelbox-formula-(for-2d)

Here's another hybrid almost as if to prove that the 2D mandelbox/mandelbrot hybrid is more mandelbox-like than the pure mandelbox. But then maybe I've got something wrong somewhere  :smiley  embarrass

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twinbee
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« Reply #4 on: November 23, 2010, 04:34:53 PM »

Fantastic. Can we see the 'whole object' for each of these pictures? Look forward to more...
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bib
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« Reply #5 on: November 23, 2010, 11:01:18 PM »

A quick vid I did in order for my laptop at work not to stay too idle while I'm on the phone or in meetings smiley
This is actually a cut of a 3D box.

<a href="http://www.youtube.com/v/Vo0AbqJGFUY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Vo0AbqJGFUY&rel=1&fs=1&hd=1</a>

And this one is a real 2D image made with Mandelbulb3D, which could also be called Mandelbulb2D cheesy


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4386
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Between order and disorder reigns a delicious moment. (Paul ValÚry)
jwm-art
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« Reply #6 on: November 24, 2010, 01:03:27 AM »

Fantastic. Can we see the 'whole object' for each of these pictures? Look forward to more...

Turns out my methods were flawed so my program was not generating a proper 2D Mandelbox after all that. Doing it the proper way, but still within the confines of my program (which is tuned toward basic Mandelbrot plotting) doesn't give results I like... The Mandelbrot set is very still... I like still. But these that you appear to appreciate, maybe I'll go back to them, but the Mandelbox parameters (scale, min radius, fixed radius) are not support at the moment and now my attention has flitted back to the good old still and silent Mandelbrot set.
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