United3dArtists Archive

Really amazing what kind of quality a 3D fractal can create.

I wished there would be a program that can store those kind of details as obj
I just remember xenomorph but that could'nt create such stunning results.

Here is the site to Daniel White
http://www.skytopia.com/project/fractal/mandelbulb.html

Pretty amazing parva,
I love fractals but this is much more beautiful..

thanks for share!

Very cool! These are amazing examples.

That video at the bottom of that link was awesome too..

Here's a link to other Fractural software...

http://www.fractalforums.com/windows-fractal-software/"

Can our beloved Truespace create anything like this ...or is the polycount too deadly?

I would assume there would need to be some scritping involved.

Here's some code.....if anyone is interested in having truespace make a mandelbulb. Not even sure it is possible!


What's the formula of this thing?
There are a few subtle variations, which mostly end up producing the same kind of incredible detail. Listed below is one version. Similar to the original 2D Mandelbrot, the 3D formula is defined by:

z -> z^n + c

...but where 'z' and 'c' are hypercomplex ('triplex') numbers, representing Cartesian x, y, and z coordinates. The exponentiation term can be defined by:

{x,y,z}^n = r^n { sin(theta*n) * cos(phi*n) , sin(theta*n) * sin(phi*n) , cos(theta*n) }
...where:
r = sqrt(x^2 + y^2 + z^2)
theta = atan2( sqrt(x^2+y^2), z )
phi = atan2(y,x)

And the addition term in z -> z^n + c is similar to standard complex addition, and is simply defined by:

{x,y,z}+{a,b,c} = {x+a, y+b, z+c}

The rest of the algorithm is similar to the 2D Mandelbrot!

Here is some pseudo code of the above:

r = sqrt(x*x + y*y + z*z )
theta = atan2(sqrt(x*x + y*y) , z)
phi = atan2(y,x)

newx = r^n * sin(theta*n) * cos(phi*n)
newy = r^n * sin(theta*n) * sin(phi*n)
newz = r^n * cos(theta*n)

...where n is the order of the 3D Mandelbulb. Use n=8 to find the exact object in this article.

The formulae above is the higher power analogue to the first green object shown on the first page here, but also see the formulae on Paul Nylander's page, which corresponds to the second green object shown instead. Both produce amazing (and similar) objects when put to the higher powers.

There are also techniques to improve rendering speed as found by FractalForum.com members:

Distance estimation provided by David Makin.

Powers -2 to 4 and powers 5 to 8, without the trig, to increase speed, by Paul Nylander. Also see Karl's earlier version for power 2 to check for "divide by zero" errors for the y values. One may need to use that technique for the higher powers too.
.

Thanks for the link Marcel!!!

I checked out Subblues' Pixel Bender Plug-in for Photoshop & After Effects
and it works amazingly well.

Attached animated gif was quick result from 2 parameters key framed.

Warning, 4 Meg gif file.

well, I think this could be done in truespace, but maybe not an entire model.
The script/plugin would have to keep a count of the number of polygons
and triangles created, and just stop creating the model when a critical count
is reached.

So what you might end up with is a partial model. Which may be fine, depending
on your needs. Worth looking into.

Hey....some of these displacement mapping images in this thread:

vi ... 339#p13339"

are looking similar to this mandelbulb thread....is there a way to make a mandelbulb using displacement? or does it have to be all polygons?

Carrara can do formula models but I dunno how big you could go
here's one i did earlier

the math..

Rhino169 wrote:Hey....some of these displacement mapping images in this thread:

vi ... 339#p13339"

are looking similar to this mandelbulb thread....is there a way to make a mandelbulb using displacement? or does it have to be all polygons?

fractal soft calculate only what you see. when the cam move, each part is calculated again with new details. a soft like TS or standard 3d soft need to represent the whole fractal, witch is impossible because the number of polys is near the infinity. you will have only an object look like a fractal but not a fractal. But you can try this:
displacement mapping need too many polygos to have very little details. Maybe a first level with real polygons and bump map as a second level of details can be used to simulate something like fractal. to use the first level as displacement mapping you need to use an image witch represent the height with his levels of grey. the same image can be used as bump map with instances of material.

Cave entrance...

Very nice!

Marcel,

Yes that would work nicely I think....at least it would give the illusion of a mandelbulb.

Maybe ...if you have time, you could create a small tutorial...and then, we as a forum, could make images as a forum contest using these instructions...? Might be a fun contest to try.