Fractal model for simulation and in inflation control

Abstract

The theory of chaos and fractals are complete with each other. Fractal geometry can be seen as a language that describes models and analyzes complex forms from nature. The basics of fractal geometry are algorithms that can be visualized as structures and different forms using the computer. The simplest example of a nonlinear iteration procedure in a complex number is given by the transformation z→z². Using the transformation z→z², we reach a dynamic dichotomy: the complex plane of initial values is divided into two subsets, one with points for which the iteration escapes, called the escape set E, and the other one with points for other initial values that remain in a bounded region forever called the prisoner set P. The bound between E and P is called the Julia set of the iteration. The Julia set for the parameter c is built on the iteration  f_c(z) = z² + c. In our case study, c is a complex number of forms c = a + i ⋅ b, where a is the Consumer Price Index and b is the Inaction Rate between the years 1991-2013.