On hybrid fractal curves of the Heighway and Lévy dragon curves. (English) Zbl 1453.28007

Kamiya, Yuichi

Mishou, Hidehiko (ed.) et al., Various aspects of multiple zeta functions – in honor of Professor Kohji Matsumoto’s 60th birthday. Proceedings of the international conference, Nagoya University, Nagoya, Japan August 21–25, 2020. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 84, 161-180 (2020).

Summary: 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 \(A_k\).
For the entire collection see [Zbl 1446.11004].

MSC:

28A80	Fractals
37F05	Dynamical systems involving relations and correspondences in one complex variable

Keywords:

automaton; automatic sequence; measure; distribution function; fractal; dragon curve; approximating curve

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