Fractal Geometry and Chaos Theory: From Old Problems to New Models and Methods

Fractal geometry and chaos theory are deeply rooted in significant problems in the history of mathematics and science. While mathematicians have geometrical descriptions of space with its properties, scientists have attempted to characterize the physical properties of fundamental entities present in space and time. The separate investigations frequently influenced each other and led to profound theories, answers, and models. However, at the same time new problems repeatedly arose internal to mathematics and externally in the applications to which mathematics was applied. Fractal geometry issues from these antecedents in response to features and processes in nature not easily represented by historical mathematical models