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In [[mathematics]], '''self-affinity''' is a feature of a [[fractal]] whose pieces are [[scaling (geometry)|scaled]] by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an [[anisotropic]] [[affine transformation]].

In [[mathematics]], '''self-affinity''' is a feature of a [[fractal]] whose pieces are [[scaling (geometry)|scaled]] by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an [[anisotropic]] [[affine transformation]].

在数学中，自仿射性是分形的特征之一，分形的各部分在 x 方向和 y 方向上按不同的比例缩放。这意味着要理解这些分形对象的自相似性，必须使用'''Anisotropic Affine Transformation 各向异性仿射变换'''进行缩放。

 

==Definition 定义==

在数学中，自仿射性是分形的特征之一，它的各部分在 x 方向和 y 方向上按不同的比例缩放。这意味着，为了了解这些分形物体的自相似性，它们必须使用各向异性仿射变换重新标度。

 

 

 

==Definition==

A [[Compact space|compact]] [[topological space]] ''X'' is self-similar if there exists a [[finite set]] ''S'' indexing a set of non-[[surjective]] [[homeomorphism]]s <math>\{ f_s : s\in S \}</math> for which

A [[Compact space|compact]] [[topological space]] ''X'' is self-similar if there exists a [[finite set]] ''S'' indexing a set of non-[[surjective]] [[homeomorphism]]s <math>\{ f_s : s\in S \}</math> for which