Often fractals are characterized as objects exhibiting some type of scaling symmetry. 
However, as the filledin circle shows (area scales as radius^{2}), scaling alone does not imply fractality. 
The simplest fractals are selfsimilar with respect to scale, by which we mean that any such object satisfies the following three requirements: 



Not fractal  Fractal  
Although the blue and red outlines in the lefthand figure mark smaller copies of the large square, the overall shape can be adequately described in terms of an evenly subdivided square; specifically, it is not necessary to invoke the words "scaled" or "recursive" to explain, in a concise manner, how it is constructed. The structure of the pattern on the right clearly requires a more complicated description. 
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