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| {{Quote|In order to give an operational meaning to the property of self-similarity, we are necessarily restricted to dealing with finite approximations of the limit figure. This is done using the method which we will call box self-similarity where measurements are made on finite stages of the figure using grids of various sizes.<ref name="Classroom">Peitgen, et al (1991), p.2-3.</ref>}} | | {{Quote|In order to give an operational meaning to the property of self-similarity, we are necessarily restricted to dealing with finite approximations of the limit figure. This is done using the method which we will call box self-similarity where measurements are made on finite stages of the figure using grids of various sizes.<ref name="Classroom">Peitgen, et al (1991), p.2-3.</ref>}} |
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− | ==Self-affinity== | + | ==Self-affinity 自仿射性== |
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| <!--[[Self-affinity]] redirects directly here.--> | | <!--[[Self-affinity]] redirects directly here.--> |
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| ! -- 自我关联直接重定向到这里 -- | | ! -- 自我关联直接重定向到这里 -- |
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− | [[Image:Self-affine set.png|thumb|right| A self-affine fractal with [[Hausdorff dimension]]=1.8272.]] | + | [[Image:Self-affine set.png|thumb|right| A self-affine fractal with [[Hausdorff dimension]]=1.8272. |
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| + | 图示为一个自仿射分形,其豪斯多夫维数为1.8272.]] |
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| A self-affine fractal with [[Hausdorff dimension=1.8272.]] | | A self-affine fractal with [[Hausdorff dimension=1.8272.]] |
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| 一个自仿射分形[豪斯多夫维数1.8272. ] | | 一个自仿射分形[豪斯多夫维数1.8272. ] |
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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]]. |
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| In mathematics, self-affinity is a feature of a fractal whose pieces are 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 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. |
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− | 在数学中,自亲和力是分形的一个特征,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。
| + | 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。 |
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