On the Path to Understanding the Tortuosity of Fractal Curves

In this article, we will focus on curves and their property called tortuosity, or total generalized absolute curvature. In the first part, we deal with the known theory of curves, which is necessary to define tortuosity. We will go through the derivative of the curve, the tangent to the curve, the formula for calculating the length of the curve, reparameterization, and natural reparameterization. Finally, we come to higher derivatives and the key concepts of the first part, the curvature of a curve. From the second chapter, we will focus on our work, and introduce our definition of tortuosity and its generalization. Then we show some basic properties such as invariance with respect to the shift, rotation, and reparametrization. In the last part, we focus on the tortuosity of the fractal curves and show some possibilities, of how to calculate it. The last part was supported with the graphs created in Maple program, and also Python application which was useful for fractal curves.