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Don't know if this is really a Mandelbulb rendering, and obviously, you'll see much more 2D than 3D, but I like this fractal alot   ::) ;D
http://www.youtube.com/watch?v=O9BgtW-qFvw

Like it.. I think 2D is usually more beautiful than 3D.

mooooooore, loooooooooooooongeeeeeer, deeeeeeeeeeepeeeeeeer!
excellent!
love the zoom

was it that fractal with the mandelbrot in the x/z plane ?
love those tree structures built in !

at the end the animation of the 3d object could be slooooooooooooower!

well done!
hectic!

so, what did you use to render ?!?!

Yes it is this fractal, rendered in Ultrafractal. It's really fun to explore, because there are strong similarities with the way the Mandelbrot set is structured, but also a lot of differences.
(http://www.fractalforums.com/gallery/1/492_15_01_10_7_50_34.jpeg)

lol, i am wondering the whole time why no one rotates it 90 degrees around the x axis :)

eh voila we have a nice mandelbrot 3d candidate,what was the formula modification ? and what the heck uf formula you used ? i can not
get my uf5 ready to render a nice deeeeep anim, how do you control camera pathes ?!

I did not do anything special to the formula  ;D

This picture above uses (I think) exactly the same formula as the seminal twinbee/lycium render  :angel1:

In UF I use an MMF formula that is not public yet  :evil1: :D O0 and I just control camera path using the UF location, like you always do in 2D  :o :D

No mystery, just curiosity  O0 :angel1:

a great vid and very nice quater-cut of the mbulb :D

I will first post some images :)
(http://www.fractalforums.com/gallery/1/492_17_01_10_8_50_16.jpeg)

oh my.... where did you find that one? :D
Looks great :D

indeed,awesome maya style picture !  O0

somewhere quite deep near the border of the perpendicular Mandelbrot :)

Another one, in another area:
(http://www.fractalforums.com/gallery/1/492_17_01_10_11_03_16.jpeg)

There was a post where someone asked if several large minibrots could be seen together in a single view. It seems that this phenomenon occurs a lot more frequently in the perpendicular Mandelbrot:

(http://www.fractalforums.com/gallery/1/492_17_01_10_11_08_35.jpeg)

Another minibrot in shape of a Concorde, surrounded by crowns of flowers.

Symmetry plays in this fractal a different role than in the Mandelbrot set.

Anyone has the 2D equation for this fractal? Come on, it's easy!

(http://www.fractalforums.com/gallery/1/492_17_01_10_11_17_33.jpeg)

Did I get that last part right? You're operating in complex numbers (or at least really directly in 2D) for those? :D

If that's the case, it shouldn't be too hard to do deep zooms of plane sections if the standard m-set formula and this one get generalized :)

if the formula is r^n | phi*n | theta*n, the 2D-version should basically be where phi = 0 rather than theta... :)

Does that colouring relate to the 3D-structure directly or is the 3D-effect archeived in a different way?

In UF I use a 3D Mandelbulb formula from Dave Makin and I clip the object. I am really curious if this 2D fractal, that naturally seems to have many properties similar to the Mandelbrot set, has ever been explored? I bet it exists somewhere in the UF database as a 2D formula, anyone knows?
For coloring I guess this is a side effect of the 3D coloring.

Here is another minibrot, this one is not distorted:

(http://www.fractalforums.com/gallery/1/492_18_01_10_1_21_42.jpeg)

What kind of coloring is that? It looks incredible!!!  :w00t: :surprise: :w00t:

It's very special :):) in the above image, the black, yellow and green areas are on the image plane and colored by iterations. The greyish areas are "holes" behind the image plane that show the 3D structure of the Mandelbulb, with a high solid threshold.

If I try to program it in UF (that would be a big challenge!), is this logic correct :

I work in the xz plane, so theta=0 and y=0

I will use complex numbers to represent the xz plane.

First step is to convert into "spherical" coordinates at the intersection of the y=0 plane:

x+iz=r*e^i*phi

with r=(x²+z²)^1/2
and phi = atan2(x,z)

Then
newr= r²

and
if phi belongs to [0;pi/4] then newphi = 2 * phi
if phi belongs to [pi/4;pi/2] then newphi = pi - 2 * phi

Then translate back into complex, add c and iterate.

It's still a bit fuzzy to me. Does that sound correct?

Edit : I forgot to take into account that theta is not always 0. It is 0 if x>0 and pi if x<0.

can anyone give a hand ? :):)

Hmm, as far as I can tell, theta would act the same, but *phi* would be pi/2. If you think, theta is the latitude and phi is the longitude (correct me if it's the other way around), then in the regular MSet phi=0 and theta=atan2(z). Here, you still include the x-axis, so yes, it's in the xz plane. But theta still is the the latitude, and acts like the direction from the origin. Phi is set for the entire plane at 90 degrees, or pi/2. I don't think that could be canceled out in any way... After one iteration, it doubles to pi. The you add c, which could already bring it to anything like 3*pi/4, or any other number - after just one iteration it has a unique value  :sad1: Then y would also have a non-zero value... I guess you'd have to compute the entire thing normally, like the mandelbulb; it wouldn't be nearly as slow, though, because you only have one plane.

Thanks, but tonight I preferred looking for nice spots than doing maths :):) Maybe one day I will give it a more serious try!

In the meantime, here is a spiral, again taken from the "perpendicular Mandelbrot"

(http://www.fractalforums.com/gallery/1/492_18_01_10_10_36_34.jpeg)

amazing :D

I must admit, there rarely are images of the standard Mset which look equally interesting :D

Hmm, istnt it just like:

  x' = x*x - y*y + cx
  y' = -2 * y * Abs(x) + cy

(If you want it as 2D formula)

But dont ask me about UF programming  :D

Yes it works :)

Btw, very beautiful images and coloring.

Is the image size limiting to 512kB new, or is this just a personal degredation  :hmh:
However, i had to test this slice also, without that great coloring of UF, scaled down to 1/4 size:
(Seems to be magna cave underneath the mountains, may give a vulcan in a 4D version  :-\)

From the pictures so far, it seems like you might have discovered the Holy Grail of the 2D Mandelbrot  ;D. Can't wait to see some more pics!

I think this fractal and the function Jessy provided are very interesting for those looking for the holy grail.

Think it this way :

In the Twinbee/bugman Mandelbulb, the iteration formula in the xy plane is :

  x' = x*x - y*y + cx
  y' = 2 * x * y + cy

And in the xz plane it is :

  x' = x*x - z*z + cx
  z' = -2 * z * Abs(x) + cz

It seems to me that part of the 3D fractal effect comes from this difference and transformation of x into -Abs(x), because if we don’t use the -Abs() transformation we get the lathed Mandelbrot. So how could could find a way to keep the same classic formula in the xz plane, and avoid the lathed Mandelbrot?  

here is a picture of the same fractal, without the minus sign. It's funny to note that this shape is very often found as a minibrot in the Perpendicular Mandelbrot.

Using directly Jessy's 2D formula allows to leverage the power of UF coloring, and rendering speed, as in this attached example :)

beautiful :D

Hi
Another vid using this time the +sine variation of the Mandelbulb. The idea stays the same : cut it in half across the perpendicular plane to the classic 2D M set, then zoom/explore...

http://www.youtube.com/watch?v=xB3vITRz-f8

A picture in perspective of a "bud" in the "seahorse valley" of the perpendicular mandelbrot set:

(http://www.fractalforums.com/gallery/1/492_02_02_10_10_45_53.jpeg)

The video from which the above image was extracted:

http://www.youtube.com/watch?v=BbfFyUz5dkE

Nice video bib

I will try to do some animations with after effects and subblues pixelbender script...  O0

Yes, great vid and pic. I already wanted to ask if you are sure about the specific bulb, but it is the one  :)