#MathArtChallenge Day 61: Hilbert Curve

The challenge: Create a Hilbert curve.

Materials needed: Paper and pencil. Grid paper is helpful.
Math concepts you could explore with this challenge: exponents, fractals, geometry, sequences, symmetry, tessellations

Full disclosure, #mathartchallenge, I am, and always have been, intimidated by the Hilbert curve. It’s beautiful. It’s fascinating. But my brain just doesn’t want to process the transformations necessary. #mtbos #iteachmath pic.twitter.com/A0QK4CBj4p

— Annie Perkins (@anniek_p) May 17, 2020

And here’s a neat extension from Vincent Panteloni:

And… you don't have to start with that U shape. Any curve from (0,0) to (1,0) will do. Here with MetaPost :https://t.co/FwRpaJkY6L pic.twitter.com/ISUSrvisft

— Vincent Pantal🍩ni (@panlepan) May 17, 2020

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments! 

6.) Attend to precision. Describe, in detail, how to create the next iteration of a Hilbert Curve.

7.) Look for and make use of structure. Why do you think the Hilbert curve is described as a “space filling” curve?

8.) Look for and express regularity in repeated reasoning. How many line segments are necessary for each iteration of the Hilbert?