Geogebra e os conjuntos de Julia e Mandelbrot

Abstract

The study of fractals began with many protagonists, but none was as appealing as the Mandelbrot and Julia sets. The iterative system associated with the two sets is , c being fixed for each Julia set and for the Mandelbrot set. The Mandelbrot set is certainly the most popular fractal of contemporary mathematics. We can say that it is the most beautiful and the most complex. I should point out that what is outside the circle of radius 2 is not part of the Mandelbrot set. Moreover, for the actual c parameters with the iteration of the critical point is bounded and the Julia set is connected. Theoretically, this might require knowledge of the orbit, that is, an infinite number of iterations and if the starting point is at the captive set or not. In the chapter of complex numbers in grade 12, we can, in an informal way, without further scientific knowledge, prove the whole theory involving these sets, in which we use a lot of content taught in secondary education, such as composite functions, complex numbers and their properties. This leads students to study and examine this chapter more thoroughly, in a more appealing way, making them intervene, interact and develop their cognitive abilities. The Geogebra program and the use of its potentialities is very dependent on the pedagogical proposals that accompany its use. This program was granted for an educational environment and that is where, of course, its eventual educational potential will be more fully revealed.