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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions

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Department of Mathematics, Concordia College, Moorhead, MN 56562, USA
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Department of Chemistry, Concordia College, Moorhead, MN 56562, USA
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(3), 42; https://doi.org/10.3390/fractalfract3030042
Received: 21 June 2019 / Revised: 10 July 2019 / Accepted: 10 July 2019 / Published: 12 July 2019
Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry. This rotational symmetry is visually seen in the corresponding Julia and Mandelbrot sets. The features and characteristics of these related Julia and Mandelbrot sets are discussed and the parameter space, made with a phase rotation and offset shift, is intricately explored. Also studied in this work is the iterative dynamical map, its characteristics and its fixed points. View Full-Text
Keywords: fractals; Julia sets; lacunary functions; Mandelbrot sets; centered polygonal numbers; iterative dynamics fractals; Julia sets; lacunary functions; Mandelbrot sets; centered polygonal numbers; iterative dynamics
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MDPI and ACS Style

Mork, L.; Vogt, T.; Sullivan, K.; Rutherford, D.; Ulness, D.J. Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions. Fractal Fract 2019, 3, 42.

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