A simple and didactic method to calculate the fractal dimension - an interdisciplinary tool

TL;DR

This paper introduces a simple, didactic method for calculating the fractal dimension of two-dimensional objects, combining manual calculation with a novel smartphone-based approach suitable for high school education.

Contribution

It presents an accessible, two-step method for students to learn and determine fractal dimensions using free software and everyday technology, bridging theory and practical application.

Findings

Method is easy to understand and implement in classrooms

Combines manual and digital techniques for calculating fractal dimensions

Applicable to diverse educational settings and student levels

Abstract

Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study of fractals at the basic level are present in the literature, only few proposals for the study of real fractals exist, which does not seem reasonable in our point of view considering the wealth of the theme and its potentiality as interdisciplinary theme in math education. For this reason, in this text, we present a simple and easily assimilable method to calculate the fractal dimension of any two-dimensional object. The method is divided into two steps. In the first step, students learn how is calculated the fractal dimension of any figure and they do this manually. Next part, which according to our best knowledge is new, with respect to the application in classroom, consists in the procedure of determining the fractal dimension using a smartphone and a computer with free software \textit {imageJ} installed. This proposal is easily understandable, considering the high school curriculum, and readily replicable, considering its easy adaptation to the most diverse school realities.