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GENERATING FRACTAL PATTERNS BY USING $p$ -CIRCLE INVERSION

JOSÉ L. RAMÍREZ

Departamento de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombia

E-mail Address: josel.ramirez@ima.usergioarboleda.edu.co

Corresponding author.

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GUSTAVO N. RUBIANO

Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

E-mail Address: gnrubianoo@unal.edu.co

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BORUT JURČIČ ZLOBEC

Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia

E-mail Address: borut@fe.uni-lj.si

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https://doi.org/10.1142/S0218348X15500474Cited by:10 (Source: Crossref)

Abstract

In this paper, we introduce the $p$ -circle inversion which generalizes the classical inversion with respect to a circle ( $p = 2$ ) and the taxicab inversion $(p = 1)$ . We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the $p$ -circle inversion.

Keywords:

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