Visualizing the Newtons Fractal from the Recurring Linear Sequence with Google Colab: An Example of Brazil X Portugal Research

Abstract

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots will be investigated and analyzed, through fractal theory based on Newton's method. For that, Google Colab is used as a technological tool, collaborating to teach Fibonacci, Lucas, Mersenne, Oresme, Jacobsthal, Pell, Leonardo, Padovan, Perrin and Narayana sequences in Brazil and Portugal. It is also possible to notice the similarity of some of these sequences, in addition to relating them with some figures present and their corresponding visualization.