FRACTALS UNLEASHED
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Tutorial Chapter 2
Self Similarity
WHAT IS IT?
As you have seen with the example of the British coast, many things around us look the same way no matter how you magnify them. You can find this in tree branches, mountains, clouds, rivers, and practically everywhere else in nature. When parts of some object are similar to the entire object, we call it self-similarity. The property of self-similarity holds true for practically all of the mathematically created fractals as well.
PERFECT SELF-SIMILARITY
In many fractals, self-similarity is very obvious. The box fractal for example is composed of smaller versions of itself. When magnified,it turns out to be identical to the entire picture.
APPROXIMATE SELF-SIMILARITY
Sometimes, however, the object is not so perfectly self-similar. In such case, it is called approximate self-similarity. For example, in the famous Mandelbrot Set you cannot see identical pictures right away. However, when you start magnifying, you encounter small versions of it at all levels of magnification.