awesome variation on buddhabroth

[ker2x]

i found that on internet while googling, but i can't find information about this awesome variation...
Any tought ? i totally love it !!

[kram1032]

I can't be sure but my guess is that it's a combination of powerblend and rotation.
If you rotate the full 4D-set, a lot of stuff can be reveiled of the structure of the set

[aluminumstudios]

It looks like a very high-iteration rendering.  At high iterations it looses it's cloud-like appearance as orbits spiral and swirl and become bright, dominating the exposure.  In my own renderings it starts looking like this at around 20,000 iterations, however this particular one looks like it could be much, much, higher.

At high iterations the swirling orbits become so bright, that when leveled, darker regions could practically vanish - like how dark details can't be seen in a strongly back-lit photograph.  This could be why it doesn't seem to have the full, overall shape of a buddhabrot (particularly the lower region seems short.)

Also, a bug in my own software before I got rotation working caused renderings that resembled this one (from the same site you found) a little bit: http://www.alcyne.net/image/bbco4_0.jpg   I was never 100% sure what the bug was doing mathematically, but it could be a Julia style rendering or some kind of cut across the 4D object.  It doesn't look like a normal rotation to me.

I recently posted a rotation of an anti-buddhabrot http://www.fractalforums.com/movies-showcase-%28rate-my-movie%29/orbit-density-map-%28aka-anti-buddhabrot%29-rotation/  It's something I've been playing with a lot lately, but I haven't produced anything this high iteration yet.

[kram1032]

true, it also looks fairly highly itereated

[ker2x]

i'm running a test with 100.000 iterations.

and i plot point that are only between 10.000 and 100.000
there is definitively some similarity with the picture on the 1st post, but the shape is different.

So : it is very high iteration (for sure!) + something (that look like rotation).

[ker2x]

Mmm, i'm in doubt... the shape at the top have obvious similarity.
And the shape at the bottom is, in fact NOT SO different ...

I think that my "minimum iteration" parameter is still too low.
(and my color setting sux  )

[kram1032]

looking at it, it might be just one or two orders of magnitude more iterations and/or contrast enhanced.
It's pretty close already.
On one hand this makes me think that the limit shape might drop even more parts (limit shape = at infinite iterations) and on the other hand, I guess, mapping those points to a higher range of stops might do for a really nice HDR-like map.
Maybe even with a "smooth" wavelenght increase where low iterations correspond to deep red and very high iterations to purplish blue on the other side of the spectrum...

[Nahee_Enterprises]

i found that on internet while googling, but i can't find information about this awesome variation...
Any tought ?  i totally love it !!  

Instead of second guessing and trying several variations to reproduce the same image, why not just ask the creator about the details:

 SERGE DEJARDIN
 Rue Ruy 209
 Grace-Hollogne, Belgium 4460
 +32.42310826
 <alcyne<-here the AT SIGN ->skynet.be>
 

[Buddhi]

Some times ago I also made some experiments with Buddhabrots. Below there is some Buddhabrot rendered with 100000 iterations on mesh grid of resolution 100000x1000 (not square). Intensity of painted points was proportional to iteration count for achieving better contrast.


If image is not visible please click: http://picasaweb.google.com/buddhi1980/Fraktale#5240730154438198370

[kram1032]

at those iteration levels it becomes seriously chaotic.
Would be interesting to see a super computer calculating it further and further. Just to see how the final version *might* look like

[ker2x]

Intensity of painted points was proportional to iteration count for achieving better contrast.

I do that in my code and high iteration point make my image faded and dark.
I tought about using a logaritmic color map, but haven't tried yet.

how are you (in details) achieving so much contrast and brightness please ?

[kram1032]

In my images -  the code is rather slow, so many of them are quite noisy - I use custom gradients per colour channel.
pow(x,*something*) worked pretty well for that, if x is the intensity between 0 and 1 - this is simmilar to gamma, which you can see in various graphics programs....
However I also played with more complex gradients including sin, cos and stuff....

[ker2x]

I do that.

Code:

maxRExposure = MAXVAL(exposureRMap)
minRExposure = MINVAL(exposureRMap)
maxGExposure = MAXVAL(exposureGMap)
minGExposure = MINVAL(exposureGMap)
maxBExposure = MAXVAL(exposureBMap)
minBExposure = MINVAL(exposureBMap)
!write(*,*) maxRExposure, minRExposure, maxGExposure, minGExposure, maxBExposure, minBExposure
 
minExposure = MIN(minRExposure, minGExposure, minBExposure)
maxExposure = MAX(maxRExposure, maxGExposure, maxBExposure)
 
exposureRMap = exposureRMap - minExposure
exposureGMap = exposureGMap - minExposure
exposureBMap = exposureBMap - minExposure
exposureRMap = (exposureRMap / REAL(maxRExposure))*intensityR 
exposureGMap = (exposureGMap / REAL(maxGExposure))*intensityG 
exposureBMap = (exposureBMap / REAL(maxBExposure))*intensityB 

basically, i check which pixel have the total cumulated highest iteration and make it the brightest point.
probleme : if there is one single pixel ith a very high plot count, the rest of the pixels become very dark.

[kram1032]

Hmmm.... I just got an idea for a colouring method and I wonder wether that would work.
It's just a single bailout value but it uses both the regular and the anti version of the Buddhabrot.
Also, and that might be the hardest part (I personally have no idea how to implement that), you need Lab colour space or similar.
You basically take the brightness values from both sets (m1=regular and m2=anti)
Then you do this:


Then you transform the brightness of either set in such a way, that the middle part is brightest and the previously most intense part is black. For instance with (assuming b to be normalized between 0...1)


Or if you map a and b from -1...1 rather than 0...1, it's

instead...

you'll notice, that this map goes from 0 - .5 or -.5 - .5. That is because the a and b channels quickly exceed gamut range and would be "more than 100%" saturate.

[stigomaster]

There is a very simple speedup you can do to double the speed of renderings. Plot the conjugates of all points in the orbit, as the set is perfectly symmetrical. I can see that a lot of you don't do this.