Applications of Cantor Set to Fractal Geometry

Fractal geometry is a subfield of mathematics that allows us to explain many of the complexities in nature. Considering this remarkable feature of fractal geometry, this study examines the Cantor set, which is one of the most basic examples of fractal geometry. First of all, the Cantor set is one of the basic examples and important structure of it. First, the generalization of Cantor set in on R, R2 and R3 are taken into consideration. Then, the given structures are examined over curve and surface theory. This approach enables to given a relationship between fractal geometry and differential geometry. Finally, some examples are established.