Inversive Diversions and Diversive Inversions

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Gregg Helt: Inversive Diversions and Diversive Inversions. In: Bridges 2017, Pages 467–470.



In this paper, we first briefly review aspects of inversive geometry and inversive fractals. Motivated by a desire to expand our geometric and artistic toolkit, we then introduce mixed-restriction limit sets as a new technique for use with iterated function systems and groups of circle inversions to create previously undiscovered 2D inversive fractals. We also apply this technique to diverse shape-based inversions that are closely related to circle inversion. Finally, we explore extending mixed-restriction limit sets and shape-based inversions into 3D to generate 3D inversive fractals.

Extended Abstract


 author      = {Gregg Helt},
 title       = {Inversive Diversions and  Diversive Inversions},
 pages       = {467--470},
 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{}}

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