In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the algorithm that enables this transformation, and the second part focuses on studying its properties.

翻译：本研究提出一种算法，该算法通过将n维Z-曲线投影至n维球面，生成了一种看似全新的数学对象。第一部分阐述实现该变换的算法，第二部分则重点研究其数学性质。