This drawing shows the relationship between the different fractals of the "Twin Dragin". The whole color patch is a #12 fractal. The #12 fractal can be broken down into a clump of 4 units of #10 fractal. These four #10 fractals are represented by 2 warm tones (pink) and 2 cool tone (blue) shapes. The #10 fractal can be further separated into 4 units of #8 fractals. This is shown in the lower right hand corner in two shades of pink. The upper left hand corner shows sixteen #6 fractals filling up the space of a #10 fractal. The #6 fractals are in 4 shades of blue. The essence of a factal design is that all higher fractals contain the lower fractals hidden in their details and edge curvatures. This is also described as self-similar.

Look at David Chow's interpretation of the Twin Dragon

This fractal design is described in Stephen Wolfram's book "A New Kind of Science" in Chapter 5 under the title "Substitution Systems and Fractals". Wolfram's book gives a good description of the geometry rule that generates the more complex fractal by repeating substitution. The geometric rule is show on page 189. Every 2 steps, the twin dragon turns 90 degrees.

Chapter 3 of Wolfram's book deals with "The World of Simple Programs". In the section about substitution systems, the subject touches on "Paper Folding Sequences". In the Notes for Chapters page 892, Stephen Wolfram gives the following description. The sequence of up and down creases in a strip of paper that is successfully folded in half is given by a substitution system; after t steps the sequence turns out to be NestList[Join[#, {0}, Reverse[1-#]]&, {0},t].


A knit piece with fractal design by Norah Gaughan,
photo by Thayer Allyson Gowdy Fluffbuff.com.
Instructions in the book "Knitting Nature".

Jurassic Park Fractal

Twin Dragon Applet by Jelena Kovacevic

Dragon curves of Jim Loy

Dragon curves of Jos Leys

Animated tiles made by David Chow

Return to Java graphics page