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Fractal

Fractal is the term which means a geometric figure featuring self-similarity, i.e. made up of several parts, each being similar to the whole figure. In a broader sense, the fractal is interpreted as an ensemble of points in Euclidean space, having a fractional metric dimension (from the viewpoint of Minkovskiy or Housedorf), or a metric dimension strictly more than the topological one.

It should be mentioned that the word “fractal” is not a mathematical term and has no common mathematical definition.
It can be used when the viewed figure has some of the features listed below:

1. Has a non-trivial structure on every scale. Therein lies the distinction from the well-formed figures (such as a circle, an ellipse, a differentiable function). If we consider a small fragment of the well-formed figure on a very large scale, it will look like a right line fragment. For the fractal, scaling-up does not lead to simplification. We will see a complex figure on every scale.

2. It is self-similar or approximately self-similar.

3. It has a fractional metric dimension or the metric dimension exceeding the topological one.

4. It can be built with the help of recursion.

Many objects in nature have fractal properties, for example, coasts, clouds, tree crowns, blood circulatory systemб and the alveolar system of both human beings and animals.

Fractals, especially on the flat, are popular due to the combination of beauty and simplicity of building with the help of a computer.

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