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HOW TO MAKE FRACTAL TILINGS AND FRACTAL REPTILES

PENG-JEN LAI

Department of Mathematics, National Kaohsiung Normal University, Yanchao Campus: No. 62, Shenjhong Rd., Yanchao Township, Kaohsiung County 824, Taiwan, R.O.C

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https://doi.org/10.1142/S0218348X09004533Cited by:2 (Source: Crossref)

Abstract

Intensive research on fractals began around 1980 and many new discoveries have been made. However, the connection between fractals, tilings and reptiles has not been thoroughly explored. This paper shows that a method, similar to that used to construct irregular tilings in ℜ² can be employed to construct fractal tilings. Five main methods, including methods in Escher style paintings and the Conway criterion are used to create the fractal tilings. Also an algorithm is presented to generate fractal reptiles. These methods provide a more geometric way to understand fractal tilings and fractal reptiles and complements iteration methods.

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