Updated September, 2022
A collection of Buddhabrot-related images and videos that I created.
The Buddhabrot's 6 major planes.
The Mandelbrot set is contained in a circle, so it can easily be turned inside out.
The Buddhabrot fits perfectly inside a 4D cube.
The formula used for the next image is Zn = Zn-13 + C.
The following images are a zoom of the '3rd eye' on the Buddha's forehead. Each B&W image takes a color channel, and merging them all results in the last one. Center at (-1.15, 0i), width = 0.125.
Zoom of the 3rd circumference on Buddha's head.
The sequence below shows a deep zoom on the floating Ghostbrots on the main figure's shoulder.
The next 2 images zoom on the Buddhabrot's center. The first image shows only orbits projected by the Minibrot centerd at (-.16, 1.035i).
Rotation through the Buddhabrot's 6 major planes.
What happens as we sample more and more points on the plane? Start with 1 point per pixel, and finish with 10000.
What happens as the value of maxN increases? Start with 1, finish with 25000.
Plane sweep. Painting only trajectories that belong to points within the height 0.1 horizontal stripe.
Rotation from plane (Cr, Ci) to (Zr, Zi). This illustrates how trajectories unfold the Mandelbrot into the Buddhabrot.
The next 3 videos show what happens when Z0 is initialized with different values.
Zr0 = 0, Zi0 increases from 0:
Zr0 increases from 0, Zi0 increases from 0:
Zr0 increases from 0, Zi0 = 0:
The 6 major planes, painting only trajectories that belong to points in M.
Inverted version of the previous planes.
A couple more renders.
The 6 major planes from Linas Vepstas' original idea, colored using the Buddhabrot technique.
The images below are the product of buggy code.
This rendering technique uses the Mandelbrot formula, but initializes Z0 to a random value instead of 0.
Buddhabrot hologram variations
The following images result from overlaying many axial cuttings of the 4D data -in other words, several images generated with different Z0 values; in planes (Zr, Cr) and (Zi, Ci) the cuts are visible as diagonal lines.
The following images have been generated using different values for Z0:
The image below represents the distance from each point to the closest point in the Mandelbrot set. Values outside M go brighter as they approach the border, whereas values inside M go darker as they approach the border.