Heighway Dragon
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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. In general, the total time to render in OpenScad and 3D print the design depends on the number of iterations. At first, I tried to render with the iteration of 5 which took for only few seconds and the total time of 3D printing using Creality Ender-3 Pro. was 3 hours. I tried more iterations in OpenScad to see how far I can go, which resulted in 13 iterations, although the render took for few minutes. And as for 3D printing, since the design have too much of complexity, I tried to scale it bigger in Ultimaker Cura and slice it, but since the triangles are too small, printing them ended up with dots even though the shape are the same as how the design should be. Citations: https://larryriddle.agnesscott.org/ifs/heighway/heighway.htm https://en.wikipedia.org/wiki/Iterated_function_system
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