Buddhabrot R&D Gallery

[richardrosenman]

Here's another similar test with a somewhat varied algorithm:


 
-Richard

[richardrosenman]

Like Ker2x's second test, this one involves computing a random c-point, and then generating new neighboring random points. Again, every 1000000 samples, a new c-point is generated and the loop starts again.

This results in very interesting 'clouds', or as Ker2x wrote, "Brownian Motion". Once again, the look is very unique but only at the early development of the Buddhabrot. After sufficient iteration time, the image will once again develop into a typical Buddhabrot render. Iteration time here was only 20 minutes.



-Richard

[kram1032]

really nice execution of this

What happens if you do this with Buddhagram in 4D fBM?

[ker2x]

Very nice

[cbuchner1]

It looks very similar when I set the variance of the Metropolis Hastings algorithm in my GPU based renderer to a very small number. Then the orbital starting coordinates stay very close to their initial values, creates bright spots and patterns like those seen in your image.

[richardrosenman]

(The anti-aliasing looks great in the source image but because I'm adjusting levels, they become a bit jagged.)

-Richard

[richardrosenman]

(The anti-aliasing looks great in the source image but because I'm adjusting levels, they become a bit jagged.)

-Richard

[richardrosenman]

It looks very similar when I set the variance of the Metropolis Hastings algorithm in my GPU based renderer to a very small number. Then the orbital starting coordinates stay very close to their initial values, creates bright spots and patterns like those seen in your image.

Would the Metropolis Hastings algorithm speed up my full Buddhabrot view? I believe it speeds up dramatically only once you start zooming in (which I cannot do yet), correct?

-Richard

[Millennium Nocturne]

An useful link to the buddhabrot solution using metropolis-hastings:
http://www.steckles.com/buddha/

[cbuchner1]

Would the Metropolis Hastings algorithm speed up my full Buddhabrot view? I believe it speeds up dramatically only once you start zooming in (which I cannot do yet), correct?

Yes, very correct.

[Millennium Nocturne]

What will happens if you mix this (Buddhabrot for the Newton Method):
http://www.openprocessing.org/visuals/?visualID=4159
with this (Newton Method Mandelbrot Set):
http://commons.wikimedia.org/wiki/File:Newton-lplane-Mandelbrot-smooth.jpg

just an idea 

[kram1032]

Millenium: What you ask for there is pretty straight forward
But the second one is a zoom. So richard can't do that yet.
I can zoom but it's a very slow process for me as I didn't do the Metropolis stuff...

Richard: Did you try the tan yet? (I'm currently rendering a ztanz one that I *think* should be the Nebulagram version of it... It sure is the coloured version but I'm not sure if I got the -gram part right, yet...)

[Millennium Nocturne]

Millenium: What you ask for there is pretty straight forward
But the second one is a zoom. So richard can't do that yet.
I can zoom but it's a very slow process for me as I didn't do the Metropolis stuff...

kram1032: Mandelbrot appears in many equations, so why only render buddhabrots from the original mandelbrot?
As for the metropolis stuff..well..it sounds like an easy thing to do (or at least what I have seen on that webpage)
http://www.steckles.com/buddha/

[kram1032]

I'm aware of that
http://kram1032.deviantart.com/gallery/#Fractals <- there. TONS of different formulas, using the buddhabrot technique to render them.
I'm currently working on an other one

[cbuchner1]

http://www.steckles.com/buddha/

The only criticism that I have with that web page is that his mathematical expressions used in the source code can be simplified greatly for computing the probabilities to use in the Markov chain. Essentially the code is calling and pow, log way unnecessarily often - slowing it down because these are expensive to compute on a CPU.