44 分形几何与连分数
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长久以来,我认为分形几何与连分数有着某种关系。
其中 n 为有限正整数,不必趋于无穷。
分形是几何的递归,连分数是算术的递归;
二者结构同源、形态同构。
无限迭代下分形面积趋于零,故面积不直接等于连分数;
但决定分形本质的相似比例,精确由有限级连分数表达。
此为数理统一的直观体现:形即是数,数即是形。