Brainfilling Curves: References

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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 fšr 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): 157Ð160. 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/