This Curve Looks Simple At First, But It Gets Complicated Quickly

Calculus Level 3

Consider the above curve as the number of steps tends to infinity. Which of the following is true:

The curve goes through every point in the unit square The curve does not go through the point \( (\frac{1}{2},\frac{1}{2}) \) The curve does not go through the point \( (\frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{3}) \) The curve does not go through the point \( ( \frac{1}{3},\frac{2}{3}) \)

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