Lozenge tiling of a C2 polygonal region sampled exactly via Coupling From The Past (CFTP) algorithm. Three rhombus types fill a five-parameter domain (b,c,d,e,h) on the triangular lattice. Controls adjust shape parameters, run perfect sampling or Glauber dynamics, toggle lozenge/dimer view, and select color palettes.
About this simulation
This simulation demonstrates Coupling from the Past (CFTP) for perfect sampling of lozenge tilings of C2 regions — a family of simply-connected polygonal domains on the triangular lattice parametrized by five parameters (b, c, d, e, h).
Acknowledgements: I thank Vadim Gorin for introducing me to these regions and for helpful discussions.
Shape
b
c
d
e
h
a = b-d+e+c =18
Display
Outline:
%
Boundary:
%
Simulation
Speed
100/s
q
Steps0
Flips0
Accept0%
Volume0
FPS0
CFTP-
Export & Legend
Quality:
85
T0
T1
T2
code
(note: parameters in the code might differ from the ones in simulation results below)-
Link to code(This simulation is interactive, written in JavaScript, see the source code of this page at the link) -
Link to code(C++ code for the simulation (compiled to WebAssembly))