What would the length of N-th iteration hilbert curve?

The length of the N-th iteration of a Hilbert curve isn't a simple formula like 2^N. It grows much faster.

Let's break it down:

* Iteration 0: The length is 1.

* Iteration 1: The length is 4.

* Iteration 2: The length is 16.

* Iteration 3: The length is 64.

You might notice a pattern: The length seems to be 4^N.

This is because each iteration quadruples the length. Each segment of the previous iteration is replaced by four segments of equal length.

Therefore, the length of the N-th iteration of a Hilbert curve is 4^N.