Grid Mapping Fractals

Fractals

The Mandelbrot Set
Flower
Flower
Big bugs have little bugs
On their backs to bite 'em,
And these bugs have smaller bugs,
And so on, ad infinitum.
Plume
Plume
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Coral
Coral
Ice
Ice
Cerebral Paisley
Cerebral Paisley
Snail
Snail

A fractal is a geometric object which has two important characteristics:

These images were created by a group of Visual Basic programs. All of them use the "double triangle" algorithm.

"Double Triangle" Fractals

The "double triangle" algorithm creates fractals in the following manner:

Begin with line segmentAB, and add point C to form a triangle. Repeat the same process by forming similar triangles on line segments AC and CB, creating points D, and E. Once again, repeat the process of creating similar triangles on the new line segments AD, DC, CE, and EB, giving rise to points F, G, H, and I.

Continue in this manner until such time as a line segment becomes shorter than a pre-defined length (usually less than one pixel in the display), and then plot a point at the midpoint of that line. Colors may vary according to how many times the triangles have been divided, that is, the "depth" of division at that point.

A true fractal would never stop dividing, of course, but would continue to infinity.

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Beak
Beak
Claw
Claw
Ferns
Ferns
Mica
Mica
Fillip
Fillip
PentaFract
PentaFract
Nebulae
Nebulae
Loops
Loops
Chromatized Flower
Chromatized Flower

Fractals

Last Updated November 18th, 2001
Web Page by Ned May (nedmay@chromatism.net)
URL http://chromatism.net/chromat/fractals.htm
All images and text are ©2001 by Edward S. May unless otherwise noted. All rights reserved.