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Aktuelle Version vom 30. Oktober 2015, 22:36 Uhr
Inhaltsverzeichnis
Reference
Gary Greenfield: Self-Avoiding Random Walks Yielding Labyrinths. In: Bridges 2015. Pages 247–252
DOI
Abstract
We modify a self-avoiding random walk model based on curvature by Chappell. This will lead us to the discovery of autonomously constructed drawings that often yield labyrinths. Labyrinth formation occurs when the sensing and avoiding feedback loop that modulates curvature promotes curve following. We add rendering effects in order to stylize our labyrinths and visualize certain aspects of our self-avoiding random walk behavior.
Extended Abstract
Bibtex
@inproceedings{bridges2015:247,
author = {Gary R. Greenfield},
title = {Self-Avoiding Random Walks Yielding Labyrinths},
pages = {247--252},
booktitle = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
year = {2015},
editor = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
isbn = {978-1-938664-15-1},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
note = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-247.html }},
url = {http://de.evo-art.org/index.php?title=Self-Avoiding_Random_Walks_Yielding_Labyrinths },
}
Used References
[1] Bosch, R., Fries, S., Puligandla, M. and Ressler, K., From path-segment tiles to loops and labyrinths, in Bridges 2013 Conference Proceedings. G. Hart et al., eds., Tessellations Publishing, Phoenix, AZ, 2013, pp. 119–126.
[2] Bosch, R., Chartier, T. and Rowan, M., Minimalist approaches to figurative maze design, preprint.
[3] Chappell, D., Taking a point for a walk: pattern formation with self-interacting curves, in Bridges 2014 Conference Proceedings. G. Greenfield et al., eds., Tessellations Publishing, Phoenix, AZ, 2014, pp. 337–340.
[4] Fenyvesi, K., Jablan, S. and Radovi´c, L., Following the footsteps of Daedelus: labyrinth studies meets visual mathematics, in Bridges 2013 Conference Proceedings. G. Hart et al., eds., Tessellations Publishing, Phoenix, AZ, 2013, pp. 361–368.
[5] Greenfield, G., Avoidance drawings evolved using virtual drawing robots, in Proceedings EvoMUSART 2015, A. Carballal, C. Johnson, and J. Nuno, eds., Springer-Verlag, Berlin, 2015, in press.
[6] Kremer, K. and Lyklema, J., Infinitely growing self-avoiding walk, Phys. Rev. Lett., 54, 1985, pp. 267– 269.
[7] Machado, P. and Pereira, L., Photogrowth: non-photorealistic renderings through ant paintings, in Proceedings of the Fourteenth International Conference on Genetic and Evolutionary Computation Conference Companion — GECCO 2012, T. Soule, ed., ACM, Press, New York, NY, 2012, pp. 233–240.
[8] Madras, N. and Slade, G., The Self-Avoiding Walk, BirkHauser, Boston, MA, 1993.
[9] Pedersen, H. and Singh. K., Organic labyrinths and mazes, in NPAR ’06 Proceedings of the 4th international symposium on non-photorealistic animation and rendering, ACM Press, New York, NY, 2006, pp. 79–86.
[10] Ross, F. and Ross, W., The Jordan curve theorem is non-trivial, Journal of Mathematics and the Arts, 5:4, 2011, pp. 213–219.
[11] Vanderzande, C., Lattice Models of Polymers, Cambridge University Press, New York, NY, 1998.
[12] Verbiese, S., Amazing labyrinths, further developments IV, in Bridges 2014 Conference Proceedings. G. Greenfield et al., eds., Tessellations Publishing, Phoenix, AZ, 2014, pp. 483–484.
Links
Full Text
http://archive.bridgesmathart.org/2015/bridges2015-247.pdf
