Fractals in nature and Mathematical Modelling

possible implications for teaching and learning Mathematics

Abstract

This article deals with fractals in nature, presenting an experience report that aimed to build fractal models, inspired by nature, verifying the possibilities of use in teaching and learning Mathematics in Basic Education. Fractals are discussed, focusing on botany, the main characteristics, such as self-similarity, used as a basis to characterize a natural fractal. The concept of Mathematical Modelling is also presented, the perceptions of some authors, and the relationship between this trend and fractals, which served as a reference for the organization and development of data analysis. The methodology is based on the characteristics of qualitative research in education and the Mathematical Modelling phases, in addition to exploratory research and documentary analysis as a basis for data production. The analysis of the data obtained during the research focused on the modelling process and the construction of the model in the GeoGebra software, through categories listed a priori, in line with the theory that underpins the research. The results showed that the constructed model can be classified as a physical analogy, and that, although it has not preserved the self-similarity characteristic of fractals, it is possible to be developed in Basic Education, and can collaborate with the teaching and learning of Mathematics.