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The Root 10 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




After coming down from seeing the amazing variety of the root9 triangle grid family, anything would seem anti-climactic. And indeed, I must report to you that the root10 family has very little to offer the eye and brain. Take a look and see for yourself. Why is this? I cannot say for sure, but I believe there must be some mathematically-relevant explanation.

I'll start with a rather non-descript specimen. It has a generator that looks like the classic Peano generator, but with a raised forearm on the right side. The distance from the origin to the elbow of the arm is root9, and the distance to the tip of the hand is root10. By taking the Peano generator and adding the waving arm, and some alternate flippings, we get the following shape:


In an attempt to add some excitement, I will pertile this specimen four times. Here it is shown at right.

Notice the alternating pattern in the generator's flippings. I found that alternating the flippings helped me to locate several gridfillers of this family. The next four specimens use this alternating trick. On the following page are three specimens. They are all gridfillers; two of them are based on a common generator shape. Notice the alternating pattern in the flippings of the genetic code. I found that alternating the flippings helped me to locate several gridfillers of this family. The next four specimens use this alternating trick. On the following page are three specimens. They are all gridfillers; two of them are based on a common generator shape.




The last two curves I will show of the root10 family is a dragon and a palindrome with dimension ~1.806.




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