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VOL. 84 | 2020 On hybrid fractal curves of the Heighway and Lévy dragon curves
Yuichi Kamiya

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Abstract

We introduce an automaton $M$ with some conditions. The automatic sequence $\{a(n)\}_{n=0}^{\infty}$ for $M$ gives a quantity $\mu_{a}$, which is similar to a measure on the unit interval. $M$ also gives an iterated function system, hence a fractal $A$ for $M$ is determined. Fractals treated in this paper are hybrids of the Heighway dragon curve and the Lévy dragon curve. We introduce a modified iterated function system to approximate $A$ by directed piecewise linear curves $A_{k}$. We will study a relation between $\mu_{a}$ and $A_{k}$.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283185

Digital Object Identifier: 10.2969/aspm/08410161

Subjects:
Primary: 28A80, 37F05

Rights: Copyright © 2020 Mathematical Society of Japan

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