String Figure Simulation with Multiresolution Wire Model

Abstract

String figure is a traditional game with a loop of a string played by hooking and/or unhooking strands of the loop from fingers to produce patterns representing certain objects. The patterns of the string figure change dynamically by the string manipulations by fingers. A computer-based method based on knot theory has been proposed to make string figure patterns. This method represents a string in the string figure as an extended knot diagram and generates string figure patterns by monotonically decreasing the number of crossing points. However, there are string figures where this method does not make the patterns correctly. In contrast, this paper proposes a method using physical simulation from the viewpoint that the string figure patterns are determined according to the tension and frictional force applied to the string. To evaluate the proposed method, we conducted two types of experiments. In the first experiments, we showed that physical simulations using an adaptive multi-resolution wire model have sufficient capability to compute the string figure patterns. In the second, we conducted experiments to make patterns for instances of the string figure. The experimental results indicate that the proposed method can correctly make the string figure patterns in most cases. We also found that the proposed method can make some of the string figure patterns that cannot be generated by conventional methods.