Gosper Curve

My first fractal I want to print is the Gosper Curve. This is a space-filling fractal that is also known by the name “flowsnake” as a twist on the word snowflake. Similar to the dragon curve, the Gosper Curve is a fractal because it is constructed by repetition of a small basic shape. Below, you can see how the basic first step of the curve repeats to become the larger and more intricate Gosper Curve.

As I mentioned earlier, this is a space-filling curve and the space that is filled by the curve is called the Gosper island. Other than this, I was not able to understand many of the properties of this fractal. I have found a simple YouTube video that demonstrates how the Gosper Curve grows:

I chose this fractal because it seemed like a relatively simple fractal to recreate. I also found some really cool designs of the Gosper Curve on Thingiverse, which you can check out here. My favorite image that I found linked to the Gosper Curve is a puzzle that someone created by printing two variations of the curve and fitting them together. I believe that this fractal would successfully print because it is similar to the dragon curve, and it is a generally flat surface.

3D Print Result

The 3D print of my fractal was pretty successful. Once I broke off some of the strings (the little pieces in between the design) I was able to stretch the design out into a line because it is all one continuous piece. This print took around 50 minutes to make but I would love to see what a larger model would look like if time allowed. Sharing my completed print on Thingiverse with the creator was really cool, I hope they check out the version of their design I printed!