14 citations · 15 across the 6 of their papers we have counts for
6 papers
Modeling snow crystal growth III: three-dimensional snowfakes
Janko Gravner, David Griffeath
We introduce a three-dimensional, computationally feasible, mesoscopic model for snow crystal growth, based on diffusion of vapor, anisotropic attachment, and a semi-liquid boundar…
Random growth models with polygonal shapes
Janko Gravner, David Griffeath
We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and…
Threshold-Range Scaling of Excitable Cellular Automata
Robert Fisch, Janko Gravner, David Griffeath
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least…
Metastability in the Greenberg-Hastings Model
Robert Fisch, Janko Gravner, David Griffeath
The Greenberg-Hastings Model (GHM) is a family of multitype cellular automata that emulate excitable media, exhibiting the nucleation and spiral formation characteristic of such co…
Threshold Growth Dynamics
Janko Gravner, David Griffeath
We study the asymptotic shape of the occupied region for monotone deterministic dynamics in d-dimensional Euclidean space parametrized by a threshold theta, and a Borel set N with…
Asymptotic Behavior of Excitable Cellular Automata
Richard Durrett, David Griffeath
We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministi…