The study of the frames of Mandelbrot sets of polynomials of the second degree as a means of developing the originality of students' thinking

Abstract

The article presents a methodology for studying the frames of Mandelbrot sets of polynomials of the second degree of a complex variable, based on the integration of analytical methods, mathematical programming and the use of computer graphics. A connection is established between the frames of the first and second orders of Mandelbrot sets of functions and with the curves – cardioid, lemniscate and circle. Algorithms for constructing the frames of the Mandelbrot sets of the functions under consideration in the MathCad mathematical package are presented. The task is to describe 3-order frames (where) of the Mandelbrot sets of functions and, which correspond to the existence of attracting fixed points of period 3. It is shown that the establishment of associative relations between classes of various mathematical objects (polynomials of a complex variable, curves, Mandelbrot sets) contributes to the development of original thinking and creative potential of students.