
doi: 10.5772/9057
Fractals are geometric shapes that repeat itself over a variety of scale sizes so the shape looks the same viewed at different scales. For such mathematical shapes B.Mandelbrot [1] introduced the term of “fractal curve”. Such a name is used to describe a family of geometrical objects that are not defined in standard Euclidean geometry. One of the key properties of a fractal curve is his self-similarity. A self-similar object appears unchanged after increasing or shrinking its size. Similarity and scaling can be obtained using an algorithm. Repeating a given operation over and over again, on ever smaller or larger scales, culminates in a self-similar structure. Here the repetitive operation can be algebraic, symbolic, or geometric, proceeding on the path to perfect self-similarity. The classical example of such repetitive construction is the Koch curve, proposed in 1904 by the Swedish mathematician Helge von Koch. Taking a segment of straight line (as initiator) and rise an equilateral triangle over its middle third, it results a so called generator. Note that the length of the generator is four-thirds the length of the initiator. Repeating once more the process of erecting equilateral triangles over the middle thirds of strait line results what is presented in figure (Figure 1). The length of the fractured line is now (4/3)2. Iterating the process infinitely many times results in a "curve" of infinite length, which although everywhere continuous is nowhere differentiable. Following Mandelbrot, such nondifferentiable curves is a fractal.
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 4 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
