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 |
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Answer the following questions:
- What would the length of the N-th iteration be? Look at the patterns made by the numbers
both before and after simplifying.
- 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?
- What is the length of this other Hilbert Curve?
- How does this compare to the first Hilbert Curve?
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