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The self-similarity structure is very common in people’s real life. For example, on the decorations of the walls, on the art works, even used by scientists to data prediction. This research first introduced some common methods to calculate the dimensions of fractals. Then illustrated some natural fractals and how to represent them with matrix transformations and matrix multiplications. Besides, this paper introduced some properties of each transformation. Afterwards, this study analyzed a classic 2D self-similar structure called Koch Curve and used the method demonstrated before better illustrated how the dimension of an artificial fractal can be calculated. According the analysis, there are more method to calculate the fractal dimension. However, only the simplest method will be introduced in this article. At last, this study described the process to applicate the fractal knowledge on coastline calculating. Moreover, there is also some discussion about the limitations the fractals and its outlooks. Overall, these results shed light on guiding further exploration of the self-similar structure applications and generating the chaos matter.
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