New Kinds of Fractal Patterns

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Douglas Dunham and John Shier: New Kinds of Fractal Patterns. In: Bridges 2017, Pages 111–116.



In the past we have shown how to create fractal patterns. We extend that work in three different directions. First we show how to create locally fractal patterns that have p6 symmetry. Then we modify the basic algorithm to orient motifs according to their positions. Finally we extend the algorithm to create a complex realistic-looking motif, producing an aesthetically pleasing pattern.

Extended Abstract


 author      = {Douglas Dunham and John Shier},
 title       = {New Kinds of Fractal Patterns},
 pages       = {111--116},
 booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
 year        = {2017},
 editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
 isbn        = {978-1-938664-22-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{}}

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:

[2] Doug Dunham and John Shier, FractalWallpaper Patterns, in Bridges 2015, Baltimore, Maryland, 2015, pp. 183–190. Also online at:

[3] Doug Dunham and John Shier, Repeating Fractal Patterns with 4-Fold Symmetry, in Bridges 2016, Jyv¨askyl¨a, Finland, 2016, pp. 523–524. Also online at:

[4] Doris Schattschneider, The Plane Symmetry Groups: Their Recognition and Notation, American Math- ematical Monthly, 85, 6, 439-450, July, 1978. Wikipedia site for wallpaper groups: group (accessed Jan. 24, 2017)


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