BOUNDARY VALUE PROBLEMS FOR THE HILBERT CURVE III

together with Margarita Kraus, JGU Mainz

Starting point at \( \left(\frac{1}{4},0\right) \) and generalizations

The startint point can be approximated from the left and from the right. From the foregoing constructions we obtain the following:

Approximation of the starting point from the left

Approximation of the starting point from the right

Summary

Left image: If we approximate the starting point from the left, then any point of red segments in the lower left subsquare is connectable with any point of the red segments lower right subsquare and with any point of the red segments of the upper left diagonal.

Right image: If we approximate the starting point from the right, then any point of red segments in the lower left subsquare is connectable with any point of the red segments lower right subsquare and with any point of the red segments of the upper left diagonal.

Further examples

The points \( \left(0,\frac{1}{4}\right) \) and \( \left(1,\frac{1}{4}\right) \) opposite to each other are connectible.

Closed curves with \( \left(\frac{1}{2},\frac{1}{4}\right) \) as starting point and end point.