On hybrid fractal curves of the Heighway and Lévy dragon curves

摘要

We introduce an automaton M with some conditions. The automatic sequence {a(n)}~∞_(n=0) for M gives a quantity μ_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 μ_a and A_k.