基于Kronecker积的分形图案设计及在望江挑花中的应用

摘要

In order to enrich the Wangjiang cross stitch pattern design,fractal pattern generation method based on matrix Kronecker product was proposed and applied to Wangjiang cross stitch pattern design.The basic patterns' matrix multilevel fractal processing was fulfilled by Boolean matrix model of cross stitch patterns and Kronecker product.The fractal patterns matrix was generated by multilevel matrix superimposition including basic pattern matrix,inverse basic pattern matrix and filling patterns matrix.The results show that patterns multilevel matrix fractal can be quickly realized by matrix Kronecker product.Different multilevel fractal patterns can be generated by matrix superimposition with the different basic patterns' matrix and filling patterns' matrix.This method expands the pattern design method of the Wangjiang cross stitch.%为了丰富望江挑花图案设计,提出一种基于矩阵Kronecker积的分形图案生成方法,并将其应用于望江挑花图案设计.在建立图案布尔矩阵模型的基础上,运用Kronecker积实现了基础图案矩阵的多级分彤处理,结合基础图案矩阵的反矩阵和填充图案矩阵的多级分形处理,并相互叠加生成分形图案矩阵.研究结果表明,运用矩阵Kronecker积可快速实现图案矩阵的多级分形处理.结合矩阵叠加处理,随基础图案、填充图案矩阵的不同,可生成各具特色的多级分形图案,该方法拓宽了望江挑花图案设计的思路.