Hex Haven

# Hex Haven
##Iterated Function System 3D Print

### Joniel Augustine Jerome
### September 16, 2024
### George Mason University
### Math 401: Mathematics Through 3D Printing

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### Introduction
Hex Haven is a hexagon-based iterated function system, represented visually. It is named for its appearance which resembles a kind of fortress. The iterative function repeats the hexagon pattern by splitting each into three hexagons on each iteration. These hexagons are translated to the center of each side of the pattern hexagon. The repetition over time results in a triangular shape near the top of the Hex Haven.

### Mathematical Background
Generally, iterated function systems are ways of generating fractals, which are infinitely repeating patterns that can be endlessly zoomed into. Formally, they are a finite set of contraction mappings. Iterated function systems make use of affine transformations, which are different from linear transformations because they can make use