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The Root 2 Family
  A chapter from Brainfilling Curves by Jeffrey Ventrella








1 Horror Vacui     2 A Very Patient Turtle Who Draws Lines     3 A Taxonomy of Fractology     4 Gallery of Specimens
Root 2 Family Root 3 Family Root 4 Square Grid Family Root 4 Triangle Grid Family
Root 5 Family No Root 6! Root 7 Family Root 8 Family
Root 9 Square Grid Family Root 9 Triangle Grid Family Root 10 Family Root 12 Family
Root 13 Square Grid Family Root 13 Triangle Grid Family Root 16 Square Grid Family Root 16 Triangle Grid Family
Root 17 and Beyond... 5 My Brain Fillith Over 6 References 7 Acknowledgements



It is time to officially introduce the first family of fractal curves: the root2 family. The first specimen I will show you is perhaps the most famous one of all: the classic dragon curve. Mandelbrot called it the "Harter-Heighway Dragon", after two mathematicians who explored it. It is sometimes referred to as the "Jurassic Park Dragon". For convenience, I will just call it the "HH Dragon". The other plane-filling curve of the root2 family is the Polya Sweep. Such a very different fractal! In fact, if we continue to fractalize these two curves to high-level teragons, the HH Dragon becomes increasingly craggy along its boundary, while the Polya Sweep becomes increasingly straight along its three sides. What's up with that?



End of chapter.



1 Horror Vacui     2 A Very Patient Turtle Who Draws Lines     3 A Taxonomy of Fractology     4 Gallery of Specimens
Root 2 Family Root 3 Family Root 4 Square Grid Family Root 4 Triangle Grid Family
Root 5 Family No Root 6! Root 7 Family Root 8 Family
Root 9 Square Grid Family Root 9 Triangle Grid Family Root 10 Family Root 12 Family
Root 13 Square Grid Family Root 13 Triangle Grid Family Root 16 Square Grid Family Root 16 Triangle Grid Family
Root 17 and Beyond... 5 My Brain Fillith Over 6 References 7 Acknowledgements




Brain-filling Curves - A Fractal Bestiary
by Jeffrey Ventrella

Distributed by Lulu.com
Cover Design by Jeffrey Ventrella 		Book web site: BrainFillingCurves.com

ISBN 978-0-9830546-2-7
Copyright © 2012 by Jeffrey Ventrella
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FractalCurves.com