Brahmabrot a simplified and expanded Buddhabrot

[matsoljare]

The last three look very interesting, some more closeups perhaps?

[Alef]

Zoomed in in Talis and Swirlbrot buddhas of previous renders.

Zooming in talis was painfully slow and there still are some undersampling. So then I scaled Swirlbrot, what effectively works as zooming in, but scaling is much faster.





For a notice. You can zoom in in buddhabrot, or you can scale a buddhabrot, it generates identic result, but scaling is much faster becouse it requires less sampling for the same result.

p.s.
Do this will improve my karma?

[kram1032]

What would be the difference between scaling and zooming?
Can you give a pseudo code example of each for comparison?

[Alef]

What would be the difference between scaling and zooming?
Can you give a pseudo code example of each for comparison?

It's this variable:
float param sizescaling
caption = "Size Scale"
default = 1
hint="Scaling here works as zooming in or out."
endparam

Im not absolutely shure how this works, it is retained variable from coppied code, but it works like scaling. sizescaling=2 means something like 2 x larger buddha. Maybe it's have something to do with more optimal use of source pixels or coloured are if compared with zoom. Maybe z=(z^2+c)/2 or z=z^2+c/2 or z=z^2/2 +c would do the same. Scaling should be conformal, so there shouln't be any distortions if compared with zoom.

The same image resolution, but a bigger fractal;) Result is like zooming in.

[kram1032]

just using a factor on the equation? That might be it, yeah...

[matsoljare]

Anyone tried using the Buddhabrot as a heigh map?

[Alef]

Probably no.
I bitt tested Buddhabrot scaling on my Brahmabrot version (speaking using keywords for ggle). Well, scaling is equaly slow as zooming in. Speed gain was only becouse of (resulting) less sample density. If sample density are equal, there is no speed advantages, so just forget scaling, I alsou removed it from formula, less coeffitients are better.
With less programming and free time at weekend I spend more time on rendering, so I got this:

Starbrot
z= z*0.5 - z^starpower + c
with starpower = 7


Swirlbrot
z=(exp(flip( frequency*cabs(z)+spin*atan2(z)) ) *z )^power  +c
with power = 3  frequency=1.5  spin=2


Zoom in:


p.s.
No photoshop, normalisation or postprocessing used for anything more than changing png to jpg. Trigonometric functions did their normalisation job well.
 

[kram1032]

Hmm... If you tweek the color-scheme and parameters, you might get something very christmassy.

What's the starpower?

[Alef]

Starpower -> star sides = polynomial power -1;) In 'normal' escape time fractal this formula with inverted c generated star like shapes. Getting colours you want  is not so easy with generated (direct) colours, but with gradient file it becomes noisy and looses it's cosmic appeal.

I saved orbit traps blog entries to read it in more relaxed home enviroment and then found interesting suprise It's pretty nice to be mentioned in blog with such great image picks, fractal knowledge and fluid language.

Buddhabrot_moshiahobrot_talis by Alef

This is from a FFs thread discussing Problems with implementing Budhabrot in UF.  There’s a whole bunch of interesting little “rough” images in it.  The Buddhabrot is a very captivating fractal as it often displays this kind of hazy but ordered kind of imagery.  The ghostly appearance and similarity to images of the Buddha have made this fractal an image class of its own.  The golden glow, the obedient sparks; something dharmic this way comes!

;Starbrot z= z*0.5 - z^5 + c Should zoom to 1/4 of this.

[Alef]

Ryan D:
Nice videos. It develops like molten glass. Throught I'm not shure how this happens.


Well, buddhabrot in Chaos Pro/UF lacks multithreading. It is pretty impossible to have multi threading in UF colour formula. Multi threading instead of step by step could increase speed of render, as this PC don't seem much burdened by simulateounos buddhabrot renders. But alsou I could be wrong.

starbrot
starpower=5, star geometry =0.12


p.s.
Now I'm thinking, is it possible to render buddhabrot with flame colour method? Its should be so. This is just slightly more advanced hits per pixel count. But something painting image according how it is hit, or from what orbit (region) it is hit. Buddhabrots probably looks as 3D becouse different orbits layers each other. But if would be turned into some meaningfull colour information.

[cKleinhuis]

Surely can you apply the flame methods, just the point finding method differs from flames i asked thargor to include buddhas in his flame renderer but sadly enough themethods differ way to much. . . I would lovehaving a buddha as ifs flame transform

So, whenit comes down to color correction using log methods for widespread countingvalues it fits perfectlyto apply themethods from classicflames

[Alef]

Buddhabrots have some simmilarities with flames, orbit density log plot. IMHO, it could use flames engine, but pixel hits could be generated not bu IFS, but by Buddhabrot method. That is IFS part switched with Buddhabrot, and colour part stays the same. Probably there are  difference extends in values extends.

In 0>1> region logarithms are useless and hyperbolic tangent works as logarithmic scale.

Fractal Flames algorithm claims that it colours flames according to internal structure of hits, latest hits are more important and alsou it depends from what region came hit. There alsou are something called Density Estimation. Maybe that could be used to smooth buddhabrots.


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=13072

[Alef]

Since this is main thread, here I link this thing together.

In short algorith is mutation of buddhabrot:
with colours generated by three colour waves, no throwing out escaping or non escaping orbits so it's faster than proper buddhabrot, and magnet (both convergent divergent) bailout.

Julia like version of this:
http://www.fractalforums.com/mandelbrot-and-julia-set/buddhabrot-quasijulia-set/

More high quality pictures with equalisation using sigmoid function:

http://www.fractalforums.com/images-showcase-(rate-my-fractal)/brahmabrot-(halfway-tobuddhabrot)-equalisated/


Very large image of rendering formula z=z^2+c;   z=z - 0.375*z/|z| ;
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=13986


Layered image
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=14157

Everything of this is in Ultra Fractal -> EM.ucl -> z Brahmabrot  or Chaos Pro - colouring -> buddhabrot -> brahmabrot.

And in Chaos Pro is a latest C++ code of algorithm: http://www.chaospro.de/formulas/display.php?fileid=238

[hgjf2]

Nice artistic pastelation of color for those fractals whick are good to send to NIRVANA
 

[Alef]

Thanks hgjf2.

Adding video, so that everything is in one thread.
<a href="http://www.youtube.com/v/y7Gf-UxqJCI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/y7Gf-UxqJCI&rel=1&fs=1&hd=1</a>