Drag to move, scroll to zoom, double-click to reset. Pick a curve, raise the level, and watch a one-dimensional line start to behave like something that wants to fill the plane.
What is drawn here is the polygon at the chosen level, not the limit curve. Every figure in the panel is computed live from the generator in fractals.html §2, except the similarity dimension, which is the formula log N / log(1/r).
The tent at 45° has similarity dimension exactly 4/3. At other angles the readout is the same formula, which is an upper bound once pieces overlap, and I have not determined where that begins. The double-visited-vertex count is a different measurement from the touching-pair counts in the chapter text (it misses places where one piece's end meets the middle of another), so the two numbers should not be compared. Exact arithmetic, fractals-verify.py and fractals-touch-count.py, is the source for anything stated in the text.
Exact checks at rational angles (fractals-angle-scan.py) found proper self-crossings in every tested tent angle except 45°, at a level that grows as the angle shrinks. I do not know whether crossings of the curve invalidate the dimension formula, so the readout at other angles stays labelled as the formula only.
Not proved: that the 45° limit satisfies the open-set condition, and so that 4/3 is its true (Hausdorff) dimension. The picture suggests contacts stay bounded; it does not show it.