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A time developing phenomenon is said to exhibit self-similarity if the numerical value of certain observable quantity <math>f(x,t)</math> measured at different times are different but the corresponding dimensionless quantity at given value of <math>x/t^z</math> remain invariant. It happens if the quantity <math>f(x,t)</math> exhibits dynamic scaling. The idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the numerical values of their sides are different however the corresponding dimensionless quantities, such as their angles, coincide.  

A time developing phenomenon is said to exhibit self-similarity if the numerical value of certain observable quantity <math>f(x,t)</math> measured at different times are different but the corresponding dimensionless quantity at given value of <math>x/t^z</math> remain invariant. It happens if the quantity <math>f(x,t)</math> exhibits dynamic scaling. The idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the numerical values of their sides are different however the corresponding dimensionless quantities, such as their angles, coincide.  

对于一个依赖时间发展的现象，如果其相关观测量<math>f(x,t)</math>在不同时间所测得的数值不同，但是对应的无量纲量在给定的<math>x/t^z</math>下保持不变，则可以说该现象具有自相似性。通常如果<math>f(x,t)</math>显示出动态缩放就会出现这种情况。

对于一个依赖时间发展的现象，如果其相关观测量<math>f(x,t)</math>在不同时间所测得的数值不同，但是对应的无量纲量在给定的<math>x/t^z</math>下保持不变，则可以说该现象具有自相似性。通常如果<math>f(x,t)</math>显示出'''Dynamic Scaling 动态缩放'''就会出现这种情况。这也是相似三角形概念的拓展和延伸。值得注意的是，即使两个三角形的边长不同，但他们的内角相等，则他们也是相似的。

一个时间发展的现象被称为自相似性，如果某个可观测量的数值，在不同时间测量的 math f (x，t) / math 是不同的，但是在给定的 math x / t ^ z / math 值下相应的无量纲量是不变的。如果数学量 f (x，t) / math 表现出动态缩放，就会发生这种情况。这个概念只是两个三角形相似性概念的延伸。请注意，如果两个三角形的边的数值不同，那么它们是相似的，但是对应的无量纲量，例如它们的角重合。

Peitgen ''et al.'' explain the concept as such:<blockquote>If parts of a figure are small replicas of the whole, then the figure is called ''self-similar''....A figure is ''strictly self-similar'' if the figure can be decomposed into parts which are exact replicas of the whole. Any arbitrary part contains an exact replica of the whole figure.</blockquote>

 

 

Since mathematically, a fractal may show self-similarity under indefinite magnification, it is impossible to recreate this physically. Peitgen ''et al.'' suggest studying self-similarity using approximations:<blockquote>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.</blockquote>This vocabulary was introduced by Benoit Mandelbrot in 1964.