# Buddhabrot gallery

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.

Nebulabrot render.

The Buddhabrot fits perfectly inside a 4D cube.

The formula used for the next image is Z_{n} = Z_{n-1}^{3} + C.

Zooming

The following images are a zoom of the '3^{rd} 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 3^{rd} 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).

More zooms.

Animations

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.

Buddhagrams.

The next 3 videos show what happens when Z_{0} is initialized with different values.

Zr_{0} = 0, Zi_{0} increases from 0:

Zr_{0} increases from 0, Zi_{0} increases from 0:

Zr_{0} increases from 0, Zi_{0} = 0:

Negative Buddhabrot

The 6 major planes, painting only trajectories that belong to points in M.

Inverted version of the previous planes.

A couple more renders.

Primitive Buddhabrot

The 6 major planes from Linas Vepstas' original idea, colored using the Buddhabrot technique.

Mutant Buddhabrots

The images below are the product of buggy code.

Buddhabrot hologram

This rendering technique uses the Mandelbrot formula, but initializes Z_{0} 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 Z_{0} 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 Z_{0}:

Distance estimators

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.