Hinged Truchet tiling fractals

TL;DR

This paper introduces a novel hinged tiling method for generating space-filling fractal dragon curves, ensuring tessellation and non-self-crossing properties, along with a new algorithm for fractal boundary dimension computation.

Contribution

The paper presents a new hinged tiling approach for fractal dragon curves and an innovative algorithm to compute their fractal boundary dimensions.

Findings

Fractal curves tessellate without crossing themselves.

Hinged tiling method guarantees non-self-crossing fractals.

New algorithm accurately computes the fractal dimension of boundaries.

Abstract

This article describes a new method of producing space filling fractal dragon curves based on a hinged tiling procedure. The fractals produced can be generated by a simple L-system. The construction as a hinged tiling has the advantage of automatically implying that the fractiles produced tessellate, and that the Heighway fractal dragon curve, and the other curves constructed by this method, do not cross themselves. This also gives a new limiting procedure to apply to certain Truchet tilings. I include the computation of the fractal dimension of the boundary of one of the curves, and describe an algorithm for computing the sim value of the fractal boundary of these curves. The curves produced are well known. The hinged tiling approach is new, as is the algorithm for computing the sim value.