An introduction to Fractal Geometry using the Geogebra software and Python

• Grant number: 20/11805-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2020
• End date: January 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tatiana Miguel Rodrigues
• Grantee: João Otávio Rodrigues Ferreira Frediani
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This work deals with an introduction to Fractal Geometry, but using the computation point of view. During the development of this project the student will come into contact with a new Geometry, different from the Euclidean learned during elementary and high school, where it is possible for objects with a fractional dimension, for example. The student will work with complex numbers and also with representation of these numbers on the plane (Julia and Mandelbrot fractal). After being theoretically familiar with the topic, he will use the Geogebra software to obtain the fractals, as well as use the Python language to obtain the same fractals and from then on make a comparison between the two modes. In this way you will be able to confront what you have theoretically learned with the visual results. The Convex Envelope problem related to the Sierpinski fractal will also be seen and worked on. This is one of the initial problems related to Computational Geometry. (AU)