Abstract: A new algorithm is proposed for 2-dimension Hilbert Space-Filling Curve（HSFC） and Z-order Space-Filling Curve（ZSFC）.Block Matrix Iteration Method（BMIM）is applied in the new algorithm.Development，applications and some basic knowledge of HSFC are introduced.The matrix express of 2-Dimension HSFC is presented and the new algorithm for HSFC is constructed.Some algorithm analysis are given，which show that the new algorithm is superior to the State Diagrams Driver Method（SDDM） for HSFC in terms of time and space complexity.Some contrast experiments between BMIM and SDDM are preformed.Numerical results show that computing time（CPUT） of BMIM is only one fourth of SDDM for 2-dimension HSFC at the same scale.

Key words: block matrix iteration, space-filling curve, state diagrams

摘要： 为解决2维空间填充曲线编码的快速生成问题，提出了一种基于块矩阵迭代的Hilbert空间填充曲线生成算法BMIM。该算法也适用于Z-order空间填充曲线生成。算法分析得出BMIM算法相对于驱动表算法具有较好的时间复杂度和空间复杂度，相应的数值对比实验结果表明，对于相同规模的2维Hilbert空间填充曲线生成BMIM算法的时间效率为驱动表算法的4倍。

关键词: 块矩阵迭代, 空间填充曲线, 状态表