A Rose By Any Other Name

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Gregg Helt: A Rose By Any Other Name. In: Bridges 2016, Pages 445–448.



Rhodonea curves, also known as rose curves, have intrigued mathematicians and artists alike since they were first described by Guido Grandi in the 18th century. In the late 20th century Maurer roses, closed polylines derived from rhodonea curves, were introduced. They are notable for the striking patterns they produce from a simple algorithm. Although Maurer roses have often been re-implemented, to date there is little published work on extending the concept since it was first described. In this paper we review previous work, then use that foundation to explore a number of extensions and generalizations of Maurer roses that we use to generate aesthetically pleasing forms.

Extended Abstract


 author      = {Gregg Helt},
 title       = {A Rose By Any Other Name...},
 pages       = {445--448},
 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=A_Rose_By_Any_Other_Name },
 note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-445.html}}

Used References

[1] G. Grandi, “Florum Geometricorum Manipulus Regiae Societati Exhibitus”, Philosophical Transactions Vol. 32, pp. 355–371, 1722.

[2] P. M. Maurer, “A Rose Is a Rose…”, The American Mathematical Monthly, Vol. 94, no. 7, pp. 631- 645, 1987.

[3] T. H. Fay, “A study in step size,” Mathematics Magazine, vol. 70, no. 2, p. 116, 1997.

[4] J. Gielis, “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” Am. J. Bot., vol. 90, no. 3, pp. 333–338, 2003.

[5] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. Princeton University Press, 2015.

[6] D. Y. Savio and E. R. Suryanarayan, “Chebychev Polynomials and Regular Polygons,” The American Mathematical Monthly, vol. 100, no. 7, pp. 657–661, 1993.

[7] J. Sharp, “Rigge Envelopes as Art Inspiration,” in Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture, Phoenix, Arizona, pp. 171–178, 2011

[8] C. H. Séquin, K. Lee, and J. Yen, “Fair, G2- and C2-continuous circle splines for the interpolation of sparse data points,” Computer-Aided Design, vol. 37, no. 2, pp. 201–211, 2005.

[9] A. Maschke, JWildfire software, 2011. Current release v2.60 (October 2015), http://jwildfire.org


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