new Buddhabrot gallery

[Eric B]

{ I forgot the password for my old account.. hence the name change }

I've created a new buddhabrot gallery:
http://www.fractalfreak.com/BuddhaCompilation/BuddhaGallery.html

Here are a few images from the gallery..

[Softology]

Interesting variations.

This may be of interest to you for getting smoother results.
http://softologyblog.wordpress.com/2011/06/26/buddhabrot-fractals/
A bunch of Buddhabrot related info and methods I found around the Internet and implemented.



Jason.

[Eric B]

My buddhabrot code does not randomly examine points within a region. Every point within a rectangular region about a minibrot is examined and contributes. To get a smoother image I would regularly examine more points within the same sized region, and then reduce the large image produced to a smaller size. Amounts to the same thing, though your approach may be faster.

There are many possible algorithms to display the density plot. Some curve fitting is required so the most visited regions do not wash out the darker areas, at minimum (my code).

One member here gives each points orbital ensemble a different color, resulting in very colorful images. Randomly sampled.

Another approach to colorizing buddhabrots is found here, two images at bottom of page:
http://shiny3d.de/mandelbrot-dazibao/Buddha/Buddha.htm

This HSV colorspace technique reveals lovely iridescent oil-on-water images.

I prefer buddhabrots where every point is examined (a uniform grid of points), though the randomly sampled ones can be beautiful also.

[cbuchner1]

Even more oil-film on water effects are obtained by mapping e.g. iteration count or orbit length to a wavelength in the visible spectrum and then to the equivalent color.

[Softology]

My buddhabrot code does not randomly examine points within a region. Every point within a rectangular region about a minibrot is examined and contributes. To get a smoother image I would regularly examine more points within the same sized region, and then reduce the large image produced to a smaller size. Amounts to the same thing, though your approach may be faster.

I prefer buddhabrots where every point is examined (a uniform grid of points), though the randomly sampled ones can be beautiful also.

The points you examine should all be within the original Mandelbrot area (between -0.5 and +2 for the real axis and -1.3 to +1.3 on the imaginary axis) otherwise you get artifacts that are not part of the real image.

The white lines in these images of yours look like artifacts from not using points covering the entire Mandelbrot.
http://www.fractalfreak.com/BuddhaCompilation/BuddhaGallery3.html
http://www.fractalfreak.com/BuddhaCompilation/BuddhaGallery30.html
An easy way to check if they are artifacts is expand your points region and see if they disappear.

The small circles in this image is caused by not having your maximum iteration count high enough so the orbits never reach the center of those circle areas
http://www.fractalfreak.com/BuddhaCompilation/BuddhaGallery2.html

Just a tip to help you get the best and most accurate images.  I had the same problems when I started rendering Buddhabrots and didn't realise until the artifacts were pointed out to me.

Jason.

[Eric B]

?

http://www.fractalfreak.com/BhuddaGallery/BhuddaInfo.html

Please copy and outline the faulty areas in the images and post back here! Appreciate.

[Softology]

OK, let me try and be more clear.

Your method tests points on the complex plane in a grid pattern.  You loop over the real and imaginary axis of the plane in even steps across a "region".

What range (ie maximum and minimum) real and imaginary coordinates do you use?  If you only use the coordinates from your current zoomed in region then you are doing it wrong.  You always need to use the range of points from the original zoomed out mandelbrot set image which is between -0.5 and +2 for the real axis and -1.3 to +1.3 on the imaginary axis.

Even once you do use the correct starting points, changing iterations and/or bailout will give different results, so your gallery images may be correct.  Or maybe there is no "this is the absolute correct rendering of this area of the buddhabrot" possible, so there is no correct or incorrect way to show the buddhabrots.

When I render the "heart" of the largest mini-buddhabrot on the real axis I get this after 220 million hits within the display area.



If you have the coordinates/iterations/bailout of one of your example images I could try rendering it and see the differences.

Jason.

[Eric B]

Again, see my about:
http://www.fractalfreak.com/BhuddaGallery/BhuddaInfo.html

All the images in my buddhabrot gallery are islands within and symmetrical about the real axis.

See my mandelbrot heart gallery. Each image there has a classic and buddhabrot component. Some of the points being considered have orbits not within the portion of the complex plane being displayed, however for the islands along the real axis most of the orbitals are within this window. Look at this page, you can see the heart of the buddhabrot corresponds to the dark region of the the classic image. They both correspond to the same region of the complex plane:
http://www.fractalfreak.com/BhuddaGallery/BhuddaGallery6.html

Changing the maximum iterations completely changes the appearance of the buddhabrot. Nature of the algorithm

nuff said!