Grid canvas showing occupied cells as dark squares on the integer quadrant, with red boundary emissions on the y-axis and blue on the x-axis. Simulates discretized t-PNG (stochastic rule 54) where rays cross or annihilate at each time step. Adjustable parameters: crossing probability t, birth probability b, boundary rates, grid size, and speed.
Discretized t-PNG Model
Description
The discrete t-PNG model (stochastic rule 54) lives on the integer quadrant {1,2,...}². It evolves as a Markov chain in continuous time t = x + y. Bernoulli processes with rates a_x and a_y on the boundaries emit rays: vertical rays from the x-axis, horizontal rays from the y-axis. When rays meet, they cross with probability t (horizontal moves up, vertical moves right) or merge and disappear with probability 1-t. Empty cells with empty left, down, and left-down neighbors can spontaneously become occupied with probability b.
This model was introduced by Tomaž Prosen (private communication).
Interaction Parameters
Boundary Rates
Simulation Control
Statistics
Time: 0
Occupied cells: 0