Buddhabrot is grainy

[ker2x]

i understand your problem.

what you seem to do is :

Code:

foreach (pixel) :
  translate pixel coordinate into complex coordinate
  if( not in mandelbrot set) then
    draw orbit
  end if
end for

you are limited to width*height potential orbits.

what you want is :

Code:

while(true)
  get a random complex point
  if( not in mandelbrot set) then
    translate orbit(in complex cordinate) into orbit(in pixel coordinate)
    draw orbit
  endif
end loop

now you have an insane amount of different to draw.
Because many many orbit may start on the same pixel but have totally different orbits.

This is one of the possible solution (we're doing that : http://en.wikipedia.org/wiki/Monte_Carlo_method ) but there is many other possibilities (some are yet to be invented  )

[PurpleBlu3s]

i understand your problem.

what you seem to do is :

Code:

foreach (pixel) :
  translate pixel coordinate into complex coordinate
  if( not in mandelbrot set) then
    draw orbit
  end if
end for

you are limited to width*height potential orbits.

what you want is :

Code:

while(true)
  get a random complex point
  if( not in mandelbrot set) then
    translate orbit(in complex cordinate) into orbit(in pixel coordinate)
    draw orbit
  endif
end loop

now you have an insane amount of different to draw.
Because many many orbit may start on the same pixel but have totally different orbits.

This is one of the possible solution (we're doing that : http://en.wikipedia.org/wiki/Monte_Carlo_method ) but there is many other possibilities (some are yet to be invented  )

What should my boundaries be for the complex number? Are they the same, but with greater precision/resolution, or do I also need to increase the range?
Thanks.

[ker2x]

you can safely choose random complex in thoses boundaries :

realMin = -2.0f;
realMax = 0.75f;
imaginaryMin = -1.5f;
imaginaryMax = 1.5f;

[ker2x]

feel free to take a look at : https://github.com/ker2x/Fortran_buddhabrot/blob/master/buddhabrot.f90
and : https://github.com/ker2x/Fortran_buddhabrot/blob/BlackAndWhite/buddhabrot.f90

certainly not the best algorithm but easy to read (even if you don't know fortran)

[PurpleBlu3s]

It was my lack of orbits that was letting me down, you were definitely right.

I've created two images, one with 20 iterations, the other with 256 so far. I used 100 million orbits.
http://dl.dropbox.com/u/16319566/20it.png - took about 40 seconds.
http://dl.dropbox.com/u/16319566/256it.png - took about 4 minutes.

[ker2x]

It was my lack of orbits that was letting me down, you were definitely right.

I've created two images, one with 20 iterations, the other with 256 so far. I used 100 million orbits.
http://dl.dropbox.com/u/16319566/20it.png - took about 40 seconds.
http://dl.dropbox.com/u/16319566/256it.png - took about 4 minutes.

Yay \o/

[PurpleBlu3s]

65 minutes, 1 billion orbits, 512 iterations:


Is this about as good as would be expected given the number of orbits and iterations?

[PurpleBlu3s]

Also, I just tried the Nebulabrot; 4 hours, 2048 iterations, 1 billion orbits:

http://dl.dropbox.com/u/16319566/2048it-1borbits.png

[ker2x]

Is this about as good as would be expected given the number of orbits and iterations?

Absolutely

Can you try to skip the rendering of the firsts 10 iterations ?
from 10 to 512.

[ker2x]

Also, I just tried the Nebulabrot; 4 hours, 2048 iterations, 1 billion orbits:

http://dl.dropbox.com/u/16319566/2048it-1borbits.png

nice

[PurpleBlu3s]

When I tried the minimum iterations 'trick', I got this sort of thing:

How should I decide the safest minimum iterations to avoid a 'damaged' Buddhabrot?

[ker2x]

When I tried the minimum iterations 'trick', I got this sort of thing:
<Quoted Image Removed>
How should I decide the safest minimum iterations to avoid a 'damaged' Buddhabrot?

Hummm... How many iterations ?
And, btw, it doesn't look damaged to me, it looks enhanced

[PurpleBlu3s]

I think I made the minimum 1/100 of the maximum but I can't remember exactly. Probably max = 1000, min = 10.

[ker2x]

I think I made the minimum 1/100 of the maximum but I can't remember exactly. Probably max = 1000, min = 10.

Then it make sense.
A mandelbrot at 10 iteration :