Taking a Point for a Walk: Pattern Formation with Self-Interacting Curves

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Chappell, David: Taking a Point for a Walk: Pattern Formation with Self-Interacting Curves. In: Greenfield, G eds. (2014) Bridges 2014 Conference Proceedings. Tessellations Publishing, Phoenix, pp. 337-340



I present a method of generating organic, 2D designs using self-avoiding, random walks. “Self-following” rules are introduced that produce repeating patterns that evolve and mutate as the walk progresses. The rate at which mutations occur influences the degree of organization and coherence in the final design.

Extended Abstract


 author      = {David Chappell},
 title       = {Taking a Point for a Walk: Pattern Formation with Self-Interacting Curves},
 pages       = {337--340},
 booktitle   = {Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture},
 year        = {2014},
 editor      = {Gary Greenfield, George Hart and Reza Sarhangi},
 isbn        = {978-1-938664-11-3},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 url         = {http://archive.bridgesmathart.org/2014/bridges2014-337.html, http://de.evo-art.org/index.php?title=Taking_a_Point_for_a_Walk:_Pattern_Formation_with_Self-Interacting_Curves }

Used References

[1] M. Annunziato, “The Nagual experiment”, (1998) Proceedings 1998 International Conference on Generative Art (ed. C. Soddu), pp. 241-251.

[2] K. Kremer and J. W. Lyklema, “Infinitely Growing Self-Avoiding Walk”, Phys. Rev. Lett., 54 (1985), pp. 267–269.

[3] N. Madras and G. Slade, The Self-Avoiding Walk, (1993), BirkHauser: Boston.

[4] J. McCormack, “Creative ecosystems,” in Computers and Creativity, (eds. J. McCormack and M. d’Inverno), Springer, Heidelberg, pp. 39-60.

[5] C. Vanderzande, Lattice Models of Polymers, (1998), Cambridge University Press: New York


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