# Sierpinski triangle

For my first fractal print, I am choosing the Sierpinski triangle. This fractal struck my interest because it creates a “tribal-like” pattern with its repeating elements. The closer you look at this triangle, the more intricate it gets! A fractal is something that contains recurring patterns of all different sizes within its original shape. The Sierpinski Triangle (according to wikipedia) is a fractal in the shape equilateral triangle, containing other replicated triangles within it. This fractal is part of the “self-similar” set because of this internal repetition.  Although I am unsure how, this set was originally formed as a curve and it can be constructed under any magnification strength.This triangle also goes by the title “Sierpinski gasket” or the “Sierpinski Sieve”.

As you can see by this above image, the Sierpinski triangle has an elaborate and intricate design. Centuries before this design was named, it was used in various architectural designs all over the world. Similar to many other kinds of fractals, this design can be constructed in many different ways such as: removing triangles, shrinking and duplication, the “chaos game” and many others. This video demonstrates one of the more common ways  to construct the triangle– by adding to a blank space.

The video helps to visualize the recurring patterns within the triangle and  how they work. Basically, the person drawing the triangles begins with locating the midpoints of the largest triangle and using them to construct a new triangle within its boundaries. This pattern continues on and on until the Sierpinski Triangle complete.

After browsing Thingiverse, I think I would definitely be able to print the “Pixelated Sierpinski triangle” , created by Arisaig (built using raster graphics instead of vector graphics). In can be used as a key chain or some sort of personalized charm/pendant. This print would be reasonable because it shows the design without making the print extremely complicated. Here is an example of a successful print:

As shown in the above picture, the size of this print is easily adjustable. I’m not quite sure what dimensions to use for 3D printing because I’m not very familiar with the scale… maybe 50mm? It is good to know that this model is easily adjustable to be printed in all different sizes. I’m looking forward to seeing how my very own Sierpinski triangle turns out!

In class I got to print my fractal: the Sierpinski triangle. We had to adjust the scale of the original design so that it would print before the end of class. It was very interesting to see how the printer formed the triangle and how precise the lines came out. After seeing some of my classmates’ work, I realized that the Sierpinski triangle can be constructed in various ways with various dimensions and depths.  Here is a link to the make: Link

I posted my “make” on thingiverse as well!

We also got to print this snowflake-like fractal, whose design was used by another member in my group. The name of this design is the “Sixfold Kotch”. It starts with a horizontal line with an upside down triangle sitting in the middle of it. From here, the fractal gets more and more complex as there are more and more iterations. It was cool to see how this fractal was made by the printer because we had to simplify the design to fit time constraints. You can see the original fractal from thingiverse here.