2021/10/03 by H Verrill, Verrill, H
Engineering · Mathematics · #28A80 #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #I.1.2 #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2110.01069
openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.