Title :
Visual Modeling and Fractal Methods in Science
Author :
Valery, S. Sekovanov ; Eugeny, I. Smirnov ; Vladimir, A. Ivkov ; Elena, M. Selezneva ; Svetlana, M. Shlyahtina
Abstract :
Modern mathematics is becoming more attractive for the education system because of the possibility to adapt its fundamental structures in applications and development of cognitive and creative abilities of the individual. Such subject are related to fractal geometry, which was "revived to life" by B. Mandelbrot beginning with the 70s of XX century. In this paper, we give applications of the elements of fractal geometry to physics and economics. Namely are investigated the graphical representations of rational mapping attractors and developed algorithms for identifying singularity Yang-Lee - as the Julia set of the renormalization transformation mappings using the programming language Pascal. Using Math Cad as computer algebra environment allows you to find fixed and repelling points of the mapping. We represent the section of code that implements the algorithm to perform the construction of the filling of the Julia set.
Keywords :
Pascal; computational geometry; fractals; physics computing; process algebra; set theory; symbol manipulation; Julia set; MathCad; Pascal programming language; code section; cognitive abilities; computer algebra environment; creative abilities; economics field; education system; fixed points; fractal geometry; fractal methods; fundamental structures; graphical representations; physics field; rational mapping attractors; renormalization transformation mappings; repelling points; science field; singularity identification; visual modeling; Chaos; Educational institutions; Equations; Fractals; Mathematical model; Julia set; attractor; fixed and critical points; fractal; orbit of a point; phase transition; the renormalization;
Conference_Titel :
Mathematics and Computers in Sciences and in Industry (MCSI), 2014 International Conference on
Print_ISBN :
978-1-4799-4744-7
DOI :
10.1109/MCSI.2014.28
