FRACTAL MODEL FOR SIMULATION AND INFLATION CONTROL
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 simp...
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Published in | Bulletin of the Transilvania University of Brașov. Series III, Mathematics, informatics, physics Vol. 7; no. 2; p. 161 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Brasov
Transilvania University of Brasov
01.07.2014
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Subjects | |
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Abstract | 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. |
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AbstractList | 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. 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 super( 2). Using the transformation z arrow right z super( 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 super( 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. |
Author | Cârstea, Claudia-Georgeta Enache-David, Nicoleta Sângeorzan, Livia |
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SubjectTerms | Algorithms Complex numbers Computer simulation Fractal analysis Fractal geometry Inflation Iterative methods Mathematical models Transformations |
Title | FRACTAL MODEL FOR SIMULATION AND INFLATION CONTROL |
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