The stochastic colored six-vertex model is an 𝔰𝔩n+1-related integrable stochastic system on a square lattice. Each path carries a "color" (an integer label), and at each vertex, two incoming paths (from the left and bottom) interact and produce two outgoing paths (going up and right) according to probabilistic rules.
The stochastic weights depend on the relative ordering of the incoming colors:
The boundary conditions place paths with colors 0, 1, 2, ..., N−1 entering from the left boundary at heights 0, 1, 2, ..., N−1, respectively. The rainbow coloring visualizes how these colored paths interact, cross, and separate as they evolve through the lattice, revealing the characteristic "arctic curve" phenomenon where paths freeze into deterministic regions.
Link to code
(C++ source code for the simulation)