FTCNC是常负曲率平面上兼具分形和tiling特征的新型几何对象。因空间的卷曲特征，且各尺度分形模板的衔接犬牙交错，其存在条件、构造方法和分形维计算，都远较欧氏分形复杂，目前尚无学者构造出具有严格数学意义的FTCNC。本项目拟以非欧几何、分形和tiling为基础，厘清FTCNC的存在条件和允许类型；鉴于FTCNC模板边界非测地线、对称集欠缺群结构的状况，引入Schwarz-Christoffel映射对模板作保形矫正，藉此克服流行构造法存在的tiling间隙和交叠缺陷；针对经典自相似维算法面临的数值溢出困境，通过推导记录FTCNC边界信息的递推矩阵，探讨其分形维的矩阵解法。本课题处于非欧几何、分形、tiling和计算方法的交叉领域，拟通过研究具有代表性的FTCNC，阐明一般型FTCNC的存在条件、构造方法及其维数计算问题，建立此类新型几何对象的基本理论框架，为其可视化提供关键的算法基础。

Fractal tiling with constant negative curvature (FTCNC) is a new kind of tiling which possesses both the characteristics of fractal and tiling. For the curly characteristic of space and various scale prototiles' zigzag connection, its existence condition, construction method and the computation of fractal dimension are far more complex than Euclidean fractals. So far nobody has successfully constructed FTCNC that of strict mathematical sense. Based on non-Euclidean geometry, fractal and tiling theory, this project plans to clarify the existence condition and construction method of FTCNC. In view of the situation that prototiles' boundaries are not geodesics and the prototile set lacks group structure, introducing numerical Schwarz-Christoffel conformal mapping to conformally correct prototiles, which aims to overcome the gap and overlap defects of popular approaches. According to the numerical overflow dilemma of the classical self-similar dimension algorithm, constructing joint recursive matrix recording boundary information and exploring the matrix solution of the fractal dimension of FTCNC. The project lies in the cross domain of the non-Euclidean geometry, fractal, tiling and computation method. We intend to study the representative FTCNC to clarify the existence condition, construction method and boundary dimension problems of general FTCNC, which aims to establish the basic theoretical framework of the new kind of geometry object and provide key algorithms for the visualization of FTCNC.