The 6 capital planes of the good ole Buddhabrot.
The Mandelbrot is contained inside a circle, so it can be easily inverted. The following planes represent the inverted Buddhabrot.
Nebulastyle colored Buddhabrot: the red channel's for high densities, green for average, and blue for low.
Since it can be read as a 4D object, the Buddhabrot fits perfectly in a fourdimensional cube.
If the usual stuff is to use the Mandelbrot function (Z_{n} = Z_{n1}^{2} + C), I've iterated a similar formula to generate this image: Z_{n} = Z_{n1}^{3} + C.
These images are an enlargement of the "third eye" on the buddha's forehead. Each grayscale image takes a color channel (red, green, blue), and merging them results in the last one. Center at (1.15, 0 i), side = 0.125.
Enlargement of the circumference above the buddha's head. Center at (1.4, 0 i), side = 0.003.
Next sequence is a pretty deep zoom on the flying ghostbrots over the main figure's shoulder.
Both images are a zoom on the center of the Buddhabrot, but for the first one only the iterates of the minibrot centered at (.16, 1.035 i) get painted.
The images below have been painted using my zooming applet. All parameters are specified, in case you want to try similar drawings.
Scan grid width: 601
Detail: Very low Center: (1.35, 0i) Width: 0.125 (32 X) MinNMaxN red: 5  1000 MinNMaxN green: 10  3500 MinNMaxN blue: 15  6000 

Scan grid width: 601
Detail: Very low Center: (0.158428, 1.03335i) Width: 0.030476 (~131.25 X) MinNMaxN red: 30  12000 MinNMaxN green: 20  7000 MinNMaxN blue: 10  2000 

Scan grid width: 601
Detail: Very low Center: (1.477333, 0.0i) Width: 0.018443 (~216.9 X) MinNMaxN red: 0  15000 MinNMaxN green: 0  10000 MinNMaxN blue: 0  5000 

Scan grid width: 601
Detail: Very low Center: (1.25586, 0.38095 i) Width: 0.01054 (~379.5 X) MinNMaxN red: 0  10000 MinNMaxN green: 0  1000 MinNMaxN blue: 0  500 

Scan grid width: 1501
Detail: Very low Center: (0.0728025227119999, 1.1048127150340001i) Width: 0.032 (125 X) MinNMaxN red: 20  10000 MinNMaxN green: 20  15000 MinNMaxN blue: 20  20000 

Scan grid width: 601
Detail: Very low Center: (0.1915867, 0.8151886i) Width: 0.0001165 (~34335 X) MinNMaxN red: 200  10000 MinNMaxN green: 500  25000 MinNMaxN blue: 1000  50000 
What happens as we check more and more points (Cs) on the plane. Starts with 1 C per pixel, and ends with 10000.
What happens as maxN increases (starts with 1, ends with 25000).
Plane sweep. Only iterates of points within the horizontal strip get colored (measures 0.1).
Rotation from plane (Cr,Ci) to (Zr,Zi). In other words, illustrates how iterates unfold from Mandelbrot to Buddhabrot.
Buddhagrams. The 3 clips show what happens when Z_{0} is initialized with different values.
This animation tries to synthesize everything discussed in this article: zooms and rotations in 3 and 4D. The song is "Across the Universe" from the Beatles.
Watch it on You Tube, download the torrent, download with eMule, or hit the image below for a direct download!
The 6 capital planes that result from painting the inside of the Mandelbrot with the Buddhabrot technique.
The inverted version of the previous planes.
A couple more renders.
the 6 capital planes from Linas Vepstas' original idea, colored with the Buddhabrot technique.
These images resulted from typing code on a dayafterthenightbefore.
The Buddhagram's idea is that any part of the image can be influenced by the whole 4D domain. To that effect, Z_{0} gets initialized to a random number instead of 0. For the nth time, the 6 capital planes.
These images result from superimposing several axial cuts from the 4D data set that is, several images generated with a different Z_{0}; in planes (Zr,Cr) and (Zi,Ci) you can tell the profile of some of the cuts across the diagonal plane.
The following drawings have been generated using a Z_{0} different than 0.
Mandelbrot render representing distances to the closest point on the fractal's border. Points outside the set brighten as they approach it; points inside M darken as they get closer to the border.
See Appendix 2: Interior and exterior distance bounding for the Mandelbrot.