TikZ examples

This is a random collection of TikZ examples. I wrote most of the code for some reason or another and decided to share the result – perhaps it is even useful for someone out there ...

The included pdf files are not meant to serve as documentation, they are there for convenience and should be viewed side by side with the source files if you wanna understand the TeX code. I tried to comment all crucial parts of the latter, although most if it should be pretty self-explanatory.

cay.tex – Cayley graph of Z * Z

The macro \drawGraph{n} draws the Cayley graph of F₂ = Z ∗ Z up to the n-th branching point. See Cayley graph on Wikipedia for details about Cayles graphs. Note that the (geometric realization of the) Cayley graph of F₂ is also the universal covering space of the "figure eight" space S¹ v S¹.

Compilation of cay.tex takes a while which is due to \drawGraph{9} in the middle (about eight minutes with pdflatex at my machine). If you can, use lualatex to compile because it is (at least here) twice as fast as pdflatex. Alternatively replace 9 by a smaller value.

nikolaus.tex – barycentric subdivision

There are

• \subdiv which draws the (first) barycentric subdivision of a triangle and
• \subdivrec which does the same for the n-th barycentric subdivision.
• \nikolausresidenz{n} draws a "Haus vom Nikolaus" in its n-th barycentric subdivision. (Note that pdflatex's default memory limitation is too restrictive for n=4 or higher. Therefore i compiled nikolausresidenz_n4.tex with lualatex.)

shuffle.tex – paths through an integer lattice

The macro \shuffle{p}{q} draws all (p,q)-shuffles, i.e. all shortest paths through a p x q integer lattice (from one edge to the diagonally opposite).