Welcome to the home of Mandala Explorer.

What is Mandala Explorer?

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Mandala Explorer enables you to draw various fractal image types, exploring endless possibilities by changing the parameters of the underlying equations.  It began as an attempt to create an interactive tool to draw “mandala-like” fractals such as Hopalong, and grew to include a number of other fractal types, and special effects such as animation and 3-D.


Mandala Explorer is highly interactive.  It provides instant gratification because the results are drawn in real time.  It is meant to be played with, and to produce “eye candy” which is also “brain candy.”  For example, a basic feature of chaotic systems is “sensitive dependence on initial conditions,” which is readily demonstrated by the simple orbit algorithms; the tiniest change in a parameter produces a completely different result, without any intermediate stages.

The images may be animated in several ways.  The simple two-dimensional orbit attractors are animated by shifting the color palette to produce a psychedelic light-show effect.  KAM Torus is animated by incrementing the angle parameter so that the image shimmers, transforms, and pulsates like a living being.  The three-dimensional images are rotated around their vertical axis.


The Latööcarfian fractals, like Lorenz, Rössler, and Icons, are three-dimensional.  I believe that this is an original feature of Mandala Explorer.

The Hopalong and Martin equations have had parameters added to produce a wider range of images.

The hit-count image types, Latööcarfian and Icon, may be rendered in greater detail by oversampling the image.  However, this requires much more time to generate each image and animation becomes impractical.  More detail may be obtained by using histogram equalization.

The color palette may be customized in a variety of ways.  Complex images that take some time to render may be quickly repainted with a new palette.

Images may be saved as either .bmp or .png files.  And the parameters and color palette configurations may be saved as small text files.

Includes a help file with complete information about all of the program features, controls, and menu items.

kam torus

Fractal Types

Simple Attractors:
• Chip
• Hopalong
• Martin
• Quadruptwo
• Threeply

• one lobe
• two lobe
• three lobe
• four lobe

• original
• mutation α
• mutation β
• mutation γ
• and Pickover

• Icon 1
• Icon 2

KAM Torus



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