I wanted to board train nostalgia and draw them in TikZ. And this was even easier than I imaged, as there is a library for fractal decorations! If only TikZ did the dishes. Based on the code I found in $TEXMF/tex/generic/pgf/libraries/pgflibrarydecorations.fractals.code.tex I quickly hacked together the following code:
This code must be either placed in $TEXMF/tex/generic/pgf/libraries/pgflibrarydecorations.fractals.code.tex or the file itself (or your personal contain-it-all package, just someplace where it can be found).
Now you just draw a tikzpicture with a single recursively decorated line:
which results in
I hope I got the factor right, but I guess 1/(2sqrt(2)) is the one I needed. A complete minimal working example is given:
which should result in (after pdfcrop) this output. LaTeX easily exceeds its total allocated memory, more iterations are impossible (unless you decrease the length of the line or the zooming factor, for some reason).