This week I spent hours watching the Youtube videos from Vihart and playing around with the ideas discussed. Several of the doodling patterns and connections shown blew my mind. In one video, the Hilbert Curve is mentioned and the first few iterations of it are drawn. I attempted to recreate them several times and ended up frustrated. What I eventually did realize is that each iteration of the Hilbert curve takes the previous image, shrinks it, and places identical copies of it into its four "corners" (see below).
There is obviously more to it than just sticking the shapes into the corners since each iteration is connected and becomes more tightly woven as it progresses. One thought that I had right as I realized how the Hilbert Curve was created was, "This is like Sierpinski's Triangle!" I had looked into Sierpinski's Triangle for one of my daily works. You can notice in the picture below that its premise is very similar to the Hilbert Curve.
Both of these patterns begin with one simple shape and build from that shape in order to create a complex, continuous design. I researched and came to find out that both Sierpinski's Triangle and the Hilbert Curve are fractals. I then looked into fractals and discovered that they contain self-similarity on all scales. 

Some clear differences between these two fractals are their base shapes (one is a triangle, the other an open square) and the orientation of their images. While Sierpinski's Triangle solely shrinks and shifts its components, the Hilbert Curve also involves rotations and extra "links" to connect them. 

Fractals are prevalent in the natural world. It's almost unreal how perfectly arranged some objects are. Fractals can be found in:

-peacock feathers
-blood vessels

And those are just a few! Math always amazes me, but this stuff really got me excited. I spent more time than planned (which may not be evident in my writing, sorry..) researching and just examining pictures of natural fractals.


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