Repeating Fractal Patterns with 4-Fold Symmetry

Reference

Douglas Dunham and John Shier: Repeating Fractal Patterns with 4-Fold Symmetry. In: Bridges 2016, Pages 523–524.

Abstract

Previously we described an algorithm that can fill a region with an infinite sequence of randomly placed and progressively smaller shapes, producing a fractal pattern. In this paperwe extend this algorithmto fill a fundamental region for the “wallpaper” group p4, then we tile the plane with copies of that region. This produces artistic patterns which have a pleasing combination of local randomness and global symmetry.

Bibtex

@inproceedings{bridges2016:523,
 author      = {Douglas Dunham and John Shier},
 title       = {Repeating Fractal Patterns with 4-Fold Symmetry},
 pages       = {523--524},
 booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
 year        = {2016},
 editor      = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
 isbn        = {978-1-938664-19-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 url         = {http://de.evo-art.org/index.php?title=Repeating_Fractal_Patterns_with_4-Fold_Symmetry },
 note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-523.html}}
}

Used References

[1] Doug Dunham and John Shier, The Art of Random Fractals, in Bridges Seoul, (eds. Gary Greenfield, George Hart, and Reza Sarhangi), Seoul, Korea, 2014, pp. 79–86. Also online at: http://archive.bridgesmathart.org/2014/bridges2014-79.html

[2] Doug Dunham and John Shier, FractalWallpaper Patterns, in Bridges 2015, Baltimore, Maryland, 2015, pp. 183–190. Also online at: http://archive.bridgesmathart.org/2015/bridges2015-183.html

[3] Doris Schattschneider, The Plane Symmetry Groups: Their Recognition and Notation, American Mathematical Monthly, 85, 6, 439-450, July, 1978. Wikipedia site for wallpaper groups: http://en.wikipedia.org/wiki/Wallpaper group (accessed Jan. 24, 2016)

Links

Full Text

http://archive.bridgesmathart.org/2016/bridges2016-523.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2016/bridges2016-523.html