Beturing is a "Befunge-flavoured" language for describing Turing machines; both the tape and the finite control are laid out two-dimensionally. In addition, the finite control must be expressed as a planar graph (no edge representing a transition may cross any other edge.) It was devised this way as a test of the so-called "wire-crossing problem". It turns out that there are universal Turing machines with finite controls that are planar graphs, so Beturing is Turing-complete.
# D(40, 4) # @(40, 4) $bbab$ # C(0, 0) # @(0, 0) . . . . . . *v*<*<*<*>*v aa .ab . .aa . >/*>./*^*^</*v bb .ba . .bb . >/*^./*^*^</*v $$ .$$ . .$$ . >/*^</*>*^.@*v . . . *@ *^*<*<
beturing.lua in the Beturing distribution