Heighway Dragon

Kenyu Koga
September 19, 2023
George Mason University Math 401: Mathematics Through 3D Printing

This 3D print design is for the iterated function systems which are constructing the fractals that have many copies united together. As it iterates through, the fractals get smaller and more complex.

For my design, I decided to create a Heighway Dragon. I start with the isosceles right triangle with the hypotenuse length of 1 and each leg, 1/sqrt(2), based on the Pythagorean theorem. To construct the dragon with the triangles, we add and alternate each triangle pointing in and out, so after the first triangle, we iterate by scaling by the leg and then rotate by 45, then scale by leg again but with rotation of 135 and translation of leg times 2 in the x-axis. Repeating these two process will lead to the completion of the Heighway Dragon design shown in the image. Since these will become a multiple of small triangles, I scaled them to enlarge it after the iteration module for coding.