HAUSDORFF DIMENSION OF GENERALIZED FIBONACCI WORD FRACTALS

Abstract

Fibonacci word fractals are a class of fractals that have been studied recently, though the words the fractals are generated from are well known in the combinatorics literature. The Fibonacci word can be used to draw a curve which possesses self-similarities determined by the recursive structure of the word. The Hausdorff dimension of the scaling limit of the finite Fibonacci word curves is computed for [Formula: see text]-Fibonacci curves and any drawing angle between [Formula: see text] and [Formula: see text].