Fractal-based algorithmic design of Chinese ice-ray lattices

Abstract

Chinese ice-ray lattices are perhaps one of the earliest and controlled designs of asymmetric and complex patterns applied as a traditional motif in windows. Such intricate and complex designs developed centuries back have created an evident curiosity to explore its underlying geometric rules. Some scholars used the Shape Grammar as a tool to explain and recreate similar patterns. The previous studies conceive the ice-ray lattice design as the iterative subdivisions of a polygon. However, they missed explaining this geometric quality through the discussion of fractal geometry, which can explain the shapes consuming self-similar or self-affine repetitions of itself at different scales. As a novel approach, this paper analytically focuses on the fractal characters of ice-ray lattice designs and uses fractal geometry as a unique tool for generating different types of ice-ray lattices. The significance of this study is the demonstration of the efficacy of fractal geometry and the simple geometric rule of IFS for analyzing and algorithmically modeling complex lattices and cracked-like patterns.

Key words： Ice-ray; Algorithm; Random fractals; IFS; Visual complexity; Fractal dimension