Sierpinski Triangle

For my fractal, I have chosen the Sierpinski Triangle.

According to a Wikipedia article, Wacław Sierpiński first described his self named triangle in 1915; however, the same article also notes that this fractal can be seen in designs dating back to the thirteenth century.

The article described this fractal as an attractive fixed set; unfortunately, I do not know exactly what that means. Luckily for me, the process for creating this fractal was fairly simple and I found it very interesting. The most interesting part about this fractal is that it is subdivided recursively. What this means is that, rather than parts being added to the original shape to make an intricate pattern, parts are removed. By first taking an equilateral triangle, dividing it into four smaller, equilateral triangles, and removing the one in the middle you have started the first phase of this fractal. As we remove more and more triangles, the shape becomes that much more complex. Not to mention that the number of subtractions that can be made are infinite. This can be slightly confusing to simply imagine, so below I have included a picture that shows what this fractal would look like in five phases:

While doing my research, I also found a youtube video that demonstrates the infinite qualities of this fractal. While the account that posted this video concedes that this is no illusion, I found Illusiontube‘s video very helpful when it came to visualizing the infinite:

I know that I am not very capable in the field of 3D printing, but I feel confidant in my ability to print this design. The Thingiverse page, Arisaig, has a print I am sure that even a beginner like me could handle. However, this version of the print contains a small hoop at the top, and though it does not necessarily compromise the integrity of the fractal itself, it could be seen as an infraction of the fractal’s formula. According to the page the hoop is there so that the design can be used as a pendant or charm, and if it turns out well, I may even hang it from my backpack.

3D Printing Results:

There was some trouble printing my original fractal, but because of that, I actually learned something pretty neat about Sierpinski’s Triangle. When the version I had chosen wouldn’t work, Dillon Call helped me find a version that would. This unique design subtracted what the original used as its frame, resulting in a layered effect. As you can see below, the print worked just fine and my roommate Grant was pretty excited about it.