Another Hilbert Curve
Exploration Questions

Here is a very minor change to the Hilbert Curve which produces a very different fractal.

Directions: Draw several iterations of Another Hilbert Curve, filling in the table below.

Iteration
  1  
  2  
  3  
  4  
  5  
Length          

Answer the following questions:

  1. What would the length of the N-th iteration be? Look at the patterns made by the numbers both before and after simplifying.

  2. What do you expect this different Hilbert Curve to look like? In other words, what would you expect to happen if you repeated this infinitely many times?

  3. What is the length of this other Hilbert Curve?

  4. How does this compare to the first Hilbert Curve?