Mandelbrot Monkeys' Tree Fractal (Fractoid) Curve

"Monkeys' Tree" Fractal Curve

Plate 31 from The Fractal Geometry of Nature
by Professor Benoit Mandelbrot.

Used with permission for the
Expanding Your Horizons Conference
at the University of Colorado at Boulder.

OUR EYH CONFERENCE MOTIF is this fractal-inspired design from Fractal Geometry of Nature by Professor Benoit Mandelbrot. Describing the shape of a snowflake or leaf, measuring the length of a coastline, creating beautiful pictures made of patterns within patterns ... these are all part of the study of fractals. Solving nature's puzzles often leads to fractal geometry.

GeneratorThe Monkeys' Tree Fractal Curve is not a true fractal, but rather a "decorative drawing" (a fractoid?) approximating a fractal generated by this pattern. Notice that there are only two regions in the image above: black and white -- there is a single connected white region and a single connected black region, separated by a continuous curve.

If this were a true fractal, the curve (the edge separating the black and white regions) would be "infinitely fuzzy", and infinitely long. The curve would be something between a one-dimensional line, and a two-dimensional area. In fact, the "dimension" (D) of the real fractal curve is approximately 1.8687. That's what makes it a "fractal!"

Mandelbrot offers these diagrams as a hint to the "Riddle of the Maze" presented with Plate 146, "Split Snowflake Halls".

The Fractal Geometry of Nature
Updated and revised edition, 1983.
by Benoit Mandelbrot
W.H. Freeman and Company
Hardcover - 468 pages
Cover Image (80K)

Here's a cool fractal site: Ralph's Little Fractal Page.
Use a search engine to find others!

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