Discretized t-PNG (Stochastic Rule 54)     vertex-models

Leo Petrov


Simulation Info

Discretized t-PNG (Stochastic Rule 54)     vertex-models

Leo Petrov

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
20
2.5
Statistics

Time: 0

Occupied cells: 0


code

(note: parameters in the code might differ from the ones in simulation results below)

Dear colleagues:
Feel free to use code (unless otherwise specified next to the corresponding link), data, and visualizations to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0). Some images are available in very high resolution upon request. I can also produce other simulations upon request - email me at lenia.petrov@gmail.com
This material is based upon work supported by the National Science Foundation under Grant DMS-2153869