Buddhabrot Buddhabrot
Buddhabrot images gallery
Buddhabrot

The 6 capital planes of the good ole Buddhabrot.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Cr, Zi plane

The Mandelbrot is contained inside a circle, so it can be easily inverted. The following planes represent the inverted Buddhabrot.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane

Nebula-style 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 four-dimensional cube.

If the usual stuff is to use the Mandelbrot function (Zn = Zn-12 + C), I've iterated a similar formula to generate this image: Zn = Zn-13 + C.

Zooms

These images are an enlargement of the "third eye" on the buddha's forehead. Each gray-scale 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.

maxN = 500
maxN = 5000
maxN = 50000
BuddhaZoom third eye

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.

Center at (-1.2025, .7075 i)
Side = .05
Center (-1.21775, .70845 i)
Side = .0008
Center (-1.217963, .70835 i)
Side = .000016
C (-1.2179607, .70834436 i)
Side = .00000024

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.

Center at (0, 0 i) Side = .3
Minibrot iterates only
Center (0, 0 i) Side = .3
All iterates

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)
MinN-MaxN red: 5 - 1000
MinN-MaxN green: 10 - 3500
MinN-MaxN blue: 15 - 6000
Scan grid width: 601
Detail: Very low
Center: (-0.158428, 1.03335i)
Width: 0.030476 (~131.25 X)
MinN-MaxN red: 30 - 12000
MinN-MaxN green: 20 - 7000
MinN-MaxN blue: 10 - 2000
Scan grid width: 601
Detail: Very low
Center: (-1.477333, 0.0i)
Width: 0.018443 (~216.9 X)
MinN-MaxN red: 0 - 15000
MinN-MaxN green: 0 - 10000
MinN-MaxN blue: 0 - 5000
Scan grid width: 601
Detail: Very low
Center: (-1.25586, 0.38095 i)
Width: 0.01054 (~379.5 X)
MinN-MaxN red: 0 - 10000
MinN-MaxN green: 0 - 1000
MinN-MaxN blue: 0 - 500
Scan grid width: 1501
Detail: Very low
Center: (0.0728025227119999, -1.1048127150340001i)
Width: 0.032 (125 X)
MinN-MaxN red: 20 - 10000
MinN-MaxN green: 20 - 15000
MinN-MaxN blue: 20 - 20000
Scan grid width: 601
Detail: Very low
Center: (-0.1915867, 0.8151886i)
Width: 0.0001165 (~34335 X)
MinN-MaxN red: 200 - 10000
MinN-MaxN green: 500 - 25000
MinN-MaxN blue: 1000 - 50000
Animations

What happens as we check more and more points (Cs) on the plane. Starts with 1 C per pixel, and ends with 10000.

Cs

What happens as maxN increases (starts with 1, ends with 25000).

Ns

Plane sweep. Only iterates of points within the horizontal strip get colored (measures 0.1).

Sweep

Rotation from plane (Cr,Ci) to (Zr,Zi). In other words, illustrates how iterates unfold from Mandelbrot to Buddhabrot.

Rotating (Cr, Ci) to (Zr, Zi)

Buddhagrams. The 3 clips show what happens when Z0 is initialized with different values.

Zr0 = 0
Zi0 = Grows from 0
Zr0 = Grows from 0
Zi0 = 0
Zr0 = Grows from 0
Zi0 = Grows from 0

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!

BuddhAnimation
Negative Buddhabrot

The 6 capital planes that result from painting the inside of the Mandelbrot with the Buddhabrot technique.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane

The inverted version of the previous planes.

Zr, Zi plane
Zr, Cr plane
Zr, Zi plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane

A couple more renders.

Primitive Buddhabrot

the 6 capital planes from Linas Vepstas' original idea, colored with the Buddhabrot technique.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane
Mutant Buddhabrots

These images resulted from typing code on a day-after-the-night-before.

Buddhagram

The Buddhagram's idea is that any part of the image can be influenced by the whole 4D domain. To that effect, Z0 gets initialized to a random number instead of 0. For the nth time, the 6 capital planes.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane
Buddhagram variants

These images result from superimposing several axial cuts from the 4D data set -that is, several images generated with a different Z0; in planes (Zr,Cr) and (Zi,Ci) you can tell the profile of some of the cuts across the diagonal plane.

Zr, Zi plane
Zr, Cr plane
Zr, Ci plane
Cr, Ci plane
Cr, Zi plane
Zi, Ci plane

The following drawings have been generated using a Z0 different than 0.

Zr0 = .5, Zi0 = 0
Zr0 = 0, Zi0 = .5
Zr0 = .5, Zi0 = .5
Zr0 = Cr, Zi0 = 0
Zr0 = 0, Zi0 = Ci
Zr0 = +Cr^.5, Zi0 = +Ci^.5
Zr0 = sin Ci, Zi0 = sin Cr
Zr0 = sin Cr, Zi0 = cos Ci
Zr0 = cos Cr, Zi0 = cos Ci
Zr0 = cos Cr, Zi0 = sin Ci
Z0 = sin complex(Ci, Cr i)
Zr0 = sin Cr, Zi0 = sin Ci
Zr0 = Ci, Zi0 = Cr
Zr0 = Ci, Zi0 = Cr
Zr0 = -Cr, Zi0 = Ci
Mandelbrot distance estimators

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.

 
Copyright © Albert Lobo Cusidó 2006-2014