Performing a multi-stage mathematical information task "Framing the Mandelbrot set of families of polynomials of the third degree and remarkable curves"

Abstract

In this article, within the framework of a multi-stage mathematical information task, the methodology for students to study Mandelbrot sets and frames of Mandelbrot sets of a family of polynomials of the third degree is indicated. Algorithms for constructing these sets in various environments are described. The connections of the frames of the Mandelbrot set with remarkable curves are studied: lemniscate, epicycloid and others. This work is aimed at developing students' creativity and research competencies. When performing a multi-stage mathematical and informational task, the student acts as a mathematician, programmer and computer artist, which is aimed at developing his creativity and increasing motivation for mathematics and programming.