FRACTAL MODEL FOR SIMULATION AND INFLATION CONTROL

• Published in: Bulletin of the Transilvania University of Brașov. Series III, Mathematics, informatics, physics Vol. 7; no. 2; p. 161
• Main Authors: Carstea, Claudia-Georgeta, Enache-David, Nicoleta, Sangeorzan, Livia
• Format: Journal Article
• Language: English
• Published: Brasov Transilvania University of Brasov 01.07.2014
• Subjects: Algorithms; Complex numbers; Computer simulation; Fractal analysis; Fractal geometry; Inflation; Iterative methods; Mathematical models; Transformations
• ISSN: 2065-2151

The theory of chaos and fractals are completing each other. The 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 [arrow right] z^sup 2^. Using the transformation z [arrow right] z^sup 2^, 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 bounded between E and P is called the Julia set of the iteration. The Julia set for the parameter c is built of the iteration fc(z) = z^sup 2^ + c. In our case study, c is a complex number of the form c = a + i . b, where a is the Consumer Price Index and b is the Inflation Rate between the years 1991-2013.