Help: I'm looking for an easy way to render my formula

[Kali]

Hello people, I'm new to the forum, and so in the world of fractals.
I don't know much of 3D graphics or rendering methods, so I need your help.
I've developed a simple VB.NET code to generate a 3D fractal using a formula of mine. To render it, I used the method of rendering 2d x-y cuts one over another, and using a gradient of grays to simulate the effect of depth. The results were interesting, but i need full 3d navigation to see if it really works.
I found that there are ways to render 3d fractals in Ultrafractal 5, the software I use to render my 2d fractals, but I didn't figure out how to use my custom formula, it looks complicated and I don't have much free time to spend in this (I work a lot and also my mind is a bit loaded of things and I don't want to overload it), so I'm looking for an easy way to render it. In my program I can generate a matrix of x,y,z values (kind of voxel map), perhaps some library I can use to render that data? or a 3d software that let me use the formula I want?

The formula I've used is: given the coordinates x,y,h (h=height):

init:
c1.real=h
c1.imag=x
c2.real=h
c2.imag=y

iterations:
z1=z1*z1+c1
z2=z2*z2+c2
z=z1+z2 (also z1*z2 seems to work)

And then evaluate the modulus of z just like a standard mandelbrot

I'll appreciate your help

(sorry if my english is not very good  )

[Kali]

 

[cKleinhuis]

ok, there is no easy way to render your formula

but if you are using uf5 you could be able to use the quat formulas defined by reb.ufr

you just have to write a formula which descends from the quat object in uf, defined in reb.ufr, as far as i know you do not need
to worry about derivatives of your formula, just make a ultrafractal formula which calculates your formula

... i havent done it yet, i have just glanced at the source, you can take for example acopy of the "mandelbulb" formula from the formula database
and the modify it to your needs

uf5 is slow, but as far as i know the only program which allows editing of formulas directly in runtime of the program

[Kali]

Thanks, I'll try

[Jesse]

i tried it already, but i didn't know if all Z's are complex numbers or if Z is a triplex... and how z1 and z2 are initialized.

Make it more clear for dummies like me and i put it in a formula file for m3d

[cKleinhuis]

or you just ask jesse

[Kali]

Hi Jesse... The Z's are all complex, also C1 and C2
Z1,Z2 and Z are initialized to 0
Z is just the sum of Z1 and Z2 complex numbers
Then the modulus of Z is evaluated, I used a bailout value of 8

Please if you try it, look also for the results on higher powers for Z1 and Z2

Thanks in advance...

[Jesse]

so it's a kind of linear combination of two orthogonal mandelbrots, will try tomorrow...

[Kali]

Yes, I think... this is an example of what I get with my VB application:



The projection is orthogonal, the depth is simulated with the level of brightness.

[Jesse]

here is a formula for mandelbulb3d, not really shure if it is like it should because it seems to be more symmetric than like in your image:

http://www.fractalforums.com/index.php?topic=5288.0

[Kali]

Thank you! it works!
It's not exactly what I thought it was going to be, but I like it. I'm navigating the 4-power version and it looks like a fractal mayan temple!  

The image I posted it's not symmetric because it's not the whole set, just one corner.

Thanks again for your help!

[Jesse]

ah, just a corner... then its ok.
For such a simple formula the output is not that bad i think, at least the programming was kind of fun because it fits to sse2 very well, can calculate both complex vectors at the same time  
Only the combinations with other formulas in hybrids dont work that good because i couldnt use the common triplex vector for the two complex ones... who cares  

ps: nice post processing on the big image!

[Kali]

Jesse, could you make, when you have the time, another formula file with a similar method but changing the z1 and z2 formulas for:

z1=c1^z1+c1
z2=c2^z2+c2

It's possible to do that?

If so, it will be great also to have another variable (a parameter 'm'), as a multiply factor like this:

z1=(c1^z1)*m+c1
z1=(c2^z2)*m+c2

(note if you try it: the bailout value has to be big for better results)

Just asking, I don't wanna bother you...
 
Thanks!

[Jesse]

I guess this is a formula that works well in 2d, but not really in 3d.  One thing is that you need a distance estimation to get a decent rendering and it seems to work not right on this one.
Had to implement a complex power that i got from wikipedia, looks like the attached image on a scale from -6 to 6 or something for 2d.
Maybe someone can confirm the correctness of the implemention.
 
But a try on 3d was just crap, beside of a very long render time.


The formula i already made could be also improved to be less noisy by not adding both vectors, but doing a slerp like interpolation to get a continous vector length.  This would lead to a better distance estimate and less noise... might do it toorrow.

[Kali]

Jesse, this is what I get in UF5... it's the same, except for that sphere-like shape, perhaps because of the coloring method you used?



I love the images this formula makes in 2D, and I thought that it could be implemented in 3D with the orthogonal combination.
I was expecting that with the "floor" part, this will not work at all, but I had some expectations for the shape that forms above, and that can be manipulated by the multiplier I use in the formula. For example, this little "winged demon":



Anyway theres no much complexity when zooming deep into the structures, just different patterns and spirals that has some variations from place to place but that repeats itself almost identically when zooming in, just like this:




Thanks a lot anyway for trying!

Now I want to show you my latest finding with the other formula... I was tweaking the parameters max and min iterations and I manage to render fine branches that looks like vegetation. Also there are shapes that I think are like minibrots equivalents or something... take a look:








I'll be waiting for that improved formula you are planning!

Thanks again for your concern