Date of Submission

Fall 2024

Academic Program

Mathematics

Project Advisor 1

Lauren Rose

Abstract/Artist's Statement

In this project we study the creation of fractals through the lens of linear algebra. We take similitudes, which are the components of the complete collection of affine transformations of a given fractal set that describe how the set has been moved, scaled, and rotated at each stage. We use similitudes to analyze the way in which the parts of a fractal shift in comparison to the initial set. We find that most self-similar fractals can be analyzed using similitudes, but not every group of similitudes creates a fractal. Part of this project is understanding why that occurs and what distinguishes a non-overlapping, self-similar collection of similitudes and an overlapping or non-self-similar set of similitudes.

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