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The Root 13 Square Grid 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



Now it is time to look at the root13 square grid family. I will start with a curve I discovered that is a self-avoider analogous to the Gosper curve: it requires two kinds of flippings (normal and double-flipped), and it roughly corresponds to a regular polygonal tiling - in this case, the square. Take a square of 9 squares, and attach one square on each edge. That is the tiling for this fractal curve. Since Mandelbrot referred to space-filling curves as "Peano Curves", and also referred to the Gosper Curve as "Peano-Gosper", I call this one the "13-Peano-Gosper".


There are several variations of this curve with dimension less than 2. I'll show you two on the next page, followed by a filled-in version of the second one.



I would like to nominate this as the token Palindrome Dragon of the root13 square grid family:



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

eyebrainbooks.com

FractalCurves.com