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References
  ...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


References

[0] Abelson, H., and diSessa, A. Turtle Geometry. MIT Press, 1986.

[1] Bandt, C. and Gummelt, P. Fractal Penrose Tilings I. Construction and matching rules. Aequationes Mathematicae, vol. 53, Numbers 1-2, Feb. 1997

[2] Barnsley, M. Fractals Everywhere. Academic Press, 1993.

[3] Carbajo, V. Fractal artworks published online at: http://www.carbajo.net/

[4] Fukuda, M. Shimizu and G. Nakamura, New Gosper Space Filling Curves, Proceedings of the International Conference on Computer Graphics and Imaging (CGIM2001) 34--38 . 2001

[5] Dekking, F. M. Recurrent Sets: a Fractal Formalism. Delft University of Technology, 1982.

[6] Fiedorowicz, Z. . root 4 triangle grid family triangle curve variation, published at: http://www.math.osu.edu/~fiedorow/math655/examples2.html

[7] Gardner, M. In which "monster curves" force redefinition of the word "Curve". Scientific American. 235. 1976

[8] Gelbrich, G. Fractal Penrose Tiles II: Tiles with fractal boundary as duals of penrose tiles. Aequationes Mathematicae, vol. 54, Numbers 1-2, Aug. 1997

[9] Hilbert, D. "Uber die stetige Abbildung einer Linie auf ein Flachenstuck", Math. Ann., 1891 (38), pp. 459-460.

[10] Hutchinson, J. Fractals and Self-Similarity. Indiana University Math. J. 30 (5) 713-747 1981.

[11] Karzes, T. Tiling Fractal curves published online at: http://www.karzes.com/

[12] Koch, H. "Sur une courbe continue sans tangente, obtenue par une construction geometrique elementaire." Archiv fr Matemat., Astron. och Fys. 1, 681-702, 1904

[13] Koch, H. "Une methode geometrique elementaire pour l'etude de certaines questions de la theorie des courbes planes", Acta Mathematica, Stockholm, 1906 (30), pp. 145-174.

[14] Mandelbrot, B. The Fractal Geometry of Nature. W. H. Freeman and Company. 1977

[15] Mandelbrot, B. The Fractal Geometry of Nature, 1977 (illustrating the quadric Koch Island: page 50)

[16] Mandelbrot, B. The Fractal Geometry of Nature, 1977 (describing the "Quartet": page 73)

[17] McKenna, D. Fractal artworks, available at: http://www.mathemaesthetics.com/MathArtPrints.html

[18] Peano, G. "Sur une courbe, qui remplit toute une aire plane", Mathematische Annalen 36 (1): 157160. 1890

[19] Prusinkiewicz, P. and Lindenmayer, A. The Algorithmic Beauty of Plants. Springer, 1990

[20] Sagan, H. Space-Filling Curves, Springer-Verlag, New York, 1991

[21] Schraa, W. Range Fractal, published online at: http://wolter.home.xs4all.nl/index.html

[22] Teachout, G. Spacefilling curve designs featured in the web site: http://teachout1.net/village/



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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