Welcome to Fractal Forums

hello all :)

new pictures of me "Mandelbulber 0.96"
(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_02_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_04_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_05_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_06_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_07_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_08_sauermann.jpg)

for all the great pictures love  :police: here http://forum.jotero.com/viewtopic.php?p=2236#2236

ciao
torolf

Great work, Torolf! I'm totally addicted to Mandelbulber too! Are these all just 'simple' IFS fractals? I'm obsessed with finding fractals that echo natural patterns, and some of yours do that really well. I love the last one particularly. Great colors, and awesome structures all around.Thanks for sharing!

-Jonathan

Thanks Jonathan,

the images were all made with settings/mandelbox rotated.

ciao
torolf

very nice shapes, but the coloring makes me think it's moldy bread.

great and sharp images, nice work!

hello all :)

many thanks :embarrass:
(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_09_sauermann.jpg)

ciao
torolf

Hello all :)

Here is a clearer picture of http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_08_sauermann.jpg

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_12_sauermann.jpg)

and a new :D
(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_14_sauermann.jpg)

ciao
torolf

great ones, especially the last, love the range, and details!!!

I like this a lot jotero
I am glad to see all nice images done with rotated boxes... ;)

WOW! THose are really amazing pics! The range of inticate details is truly awesome. Does anyone know when will  MAndelbulb 3D is likely to have this rotation of Mandeboxes implemented? Also, can anyone exlplain what the rotation is exactly?

Rotations do exist in Mandelbulb3D. Just select an amazing box as the first formula, and _Rotate as the second one.

As far as I understood, a rotation is simply.....a rotation ! for the current iteration, the point is rotated around each axis by the assigned angle in degrees.

By the way, I think that rotations are not commutative in 3D. So I don't know exactly in what order they are processed.

In Mandelbulber, buddhi talked about rotating angles of the folding planes, which is not the same thing as the _Rotate function in M3D I think, but it gives very similat results in essence (spirals...)

I might be totally misinterpreting :):)

Rotations are commutative in M3D. There's no difference between, say Formula 2 as 5,5,5 and Formula 3 as 0,0,0 and Formula 2 as 5,5,0 and Formula 3 as 0,0,5. (I think this sentence is not commutative, so maybe I should have placed brackets somewhere ;D). The same goes for the number of iterations. 10,10,10 once iterated is the same as 5,5,5 twice iterated.

BTW I've rotated quite a lot of Amazing Boxes but only rarely found spirals (One of the only ones was in Vorticity and that one was approximately a quarter of the size of the box, so even for me hard to miss :-S). On the other hand, I'm not looking as deep as bib sometimes does... http://www.fractalforums.com/movies-showcase-(rate-my-movie)/the-return-of-the-rotated-negative-box/ (http://www.fractalforums.com/movies-showcase-(rate-my-movie)/the-return-of-the-rotated-negative-box/)

I was not talking about this kind of commutativity, I was talking about rotation around X, then Y, then Z, is not the same as in another order. For example if you take (1,0,0) and rotate it 90° around X, then Y, then Z, you get (1,0,0), then (0,0,1), and finally (0,0,1). And if you rotate it around, say, X, then Z, then Y, you get (1,0,0), then (0,1,0), then (0,1,0). Mathematicians please correct me if I'm wrong.

Regarding your example, I'm almost sure that you are wrong. Setting [F1 as (5,5,5) and F2 as (0,0,0)] or [F1 as (5,5,0) and F2 as (0,0,5)] is not the same because of the bailout test that occurs in the middle, and decides if the point is in or out. The difference might be hardly noticeable in most cases, but I'm pretty sure that one could find an example where the impact would be clearly visible.

Then the big question: how to find spirals in rotated boxes? Just explore! I would say that they are often found in the middle of the cube's edges, but not necessarily. Another tip I would suggest if to set small rotations (no more than 10-12°), and vary their signs, but again, this is purely empirical. It's funny because one of my most beautiful spirals was the first one I stumbled upon, just after KRAFTWERK gave me the recipe of the rotated box: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3810

some of the image have amazing ptoential for big sized prints, but i think many of them lack a really good perspective, e.g. centering of interesting objects,
good outlook, there are soo amazingly interesting structures, and for example this image looks like a massive gateway
http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_06_sauermann.jpg
but, with a little changed camera perspective, the impact would be a little larger, in my eyes...

Oops... I stand corrected. Bib, You are, of course, right. I think I'll have to dive into my old books and see if there's a copy left of linear algebra 101...

And, before I forget, (and completely hi-jack the topic...), your renders are great Torolf! I especially like the somewhat subdued colouring.

yes a view is always available!
http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_15_sauermann.jpg

ciao
torolf

hello all :)

it's incredible what you can find everything! mandelbulber 0.97
(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_17_sauermann.jpg)

Larger
http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_17_sauermann.jpg

(http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_18_sauermann.jpg)

Langer
http://www.jotero.com/bilder/mandelbulber/mandelbulber_25_11_2010_18_sauermann.jpg

ciao
torolf

The first pic in the last post is a shell, each big dip has several smaller dips inside it, which have smaller dips again etc.
The second pic is awesome, and nice colours too.

If you want to structure rotations such that they are commutative, you can borrow physics' rules for momentum. A momentum is a vector that originates in the center of mass and points along the axis around which a rotational force is applied. The length of the vector represents the strength of that force. Whenever more than a single momentum affect a mass, they add commutatively just like vectors.

I have no idea if this would make for a good UI or good fractal imagery, though.

Great images Jotero!


About rotations, in Mandelbulber there are two possibilities to add rotations to Mandelbox. You can add very simple rotation of actual iteration around the origin. You can also rotate each folding plane separately. Results are similar, but rotations of folding planes give more possibilities.

OK, thanks for clarifying.

hello all,

fractal fungus :dink:
(http://www.jotero.com/bilder/mandelbulber/fractal_fungus_2011.jpg)

ciao
torolf

hello all,

What you see, it's not there!  :embarrass:
(http://www.jotero.com/bilder/mandelbulber/fractal_fungus_01_2011.jpg)

ciao
torolf

hello all  :D

For the passions of the sighted.
http://www.jotero.com/bilder/mandelbulber/fractal_fungus_01G_2011.jpg
2,390px × 1,793px

ciao
torolf

hello all :)

stereoscopic rot/cyan
(http://www.jotero.com/bilder/mandelbulber/stereoscopic_mandelbulbe_sauermann.jpg)

(http://www.jotero.com/bilder/mandelbulber/stereoscopic_mandelbulbe_sauermann_2011.jpg)

Original image :*)
http://www.jotero.com/bilder/mandelbulber/image00011.jpg

3D TV and holographic http://www.rabbitholes.com is possible ;)

ciao
torolf

Hello all,

I'm still excited about mandelbulber  :embarrass:
(http://www.jotero.com/evolution-of-genius_de/3d/mandelbulber_18_11_2011_sauermann.jpg)

ciao
torolf

Beautiful images and very anticipative. :) That was 2010...