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The Root 16 Triangle 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



Like the root16 square grid family, the root16 triangle grid family has many spacefilling curves that pertile equilateral polygons - in this case, triangles. I would like to show you a few. None of these examples are self-avoiders...but when rendered with rounded corners, they reveal some unique characteristics. The next four specimens each have a segment of length 2 that lies horizontally across the middle of the 4x4 triangle that houses the generator. This horizontal segment is responsible for extending the curve upward towards the pinnacle - increasingly with each fractal level.






On the next three pages are triangular specimens that I have rendered in color. The last one has the top one-fourth of the triangle rotated 180 degrees and enlarged, to its right.







Here are some non-triangle specimens with three-way symmetry. These tightly-coiled curves are of the dense variety that evade being pulled apart to breathe by way of rounded corners. But they do have interesting chambers. The second specimen is rendered with its various chambers colored in a playful manner.



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