Pythagorean Tree

Jared Bergan
27 September 2021
George Mason University Math 401

This week in Math 401: Mathematics Through 3D Printing, iterated function systems!
IFSs are the most common way for generating fractals using self-similarity in mathematics and consist of transformations such as rotations, scalings, and translations. Simply put, they are a set of transformations that make things smaller and can get infinitely small in the right circumstances.

For this project I decided to create a Pythagorean tree. Starting with a base square of length L, a triangle is placed on top with L being the hypotenuse. From there, the two other sides (which are of equal length) are now the sides of two new squares of length sqrt(L^2/2) that are generated off the one. This process can continue infinitely with two squared being made off each previous square. Since each triangle is a 45-45-90 we see that each following iterative step rotates the squares by 45 degrees resulting in a tree shape with a suffici