24 citations · 86 across the 27 of their papers we have counts for
35 papers
Two-stage Bootstrap Percolation
Zihao Fang, Janko Gravner, David Sivakoff
We introduce and study two variants of two-stage growth dynamics in with state space . In each variant, vertices in state can be change…
Polluted Modified Bootstrap Percolation
Janko Gravner, Alexander Holroyd, Sangchul Lee +1
In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability or closed with probability . A site b…
Young domination on Hamming rectangles
Janko Gravner, Matjaž Krnc, Martin Milanič +1
We introduce a family of domination-type problems in Cartesian products of two graphs. The framework captures several well-studied topics, including variants of bootstrap percolati…
Competing deterministic growth models in two dimensions
Janko Gravner, David Sivakoff
We consider three-state cellular automata in two dimensions in which two colored states, blue and red, compete for control of the empty background, starting from low initial densit…
Two-dimensional supercritical growth dynamics with one-dimensional nucleation
Daniel Blanquicett, Janko Gravner, David Sivakoff +1
We introduce a class of cellular automata growth models on the two-dimensional integer lattice with finite cross neighborhoods. These dynamics are determined by a Young diagram $\m…
Weakly robust periodic solutions of one-dimensional cellular automata with random rules
Janko Gravner, Xiaochen Liu
We study -neighbor one-dimensional cellular automata with a large number of states and randomly selected rules. We focus on the rules with weakly robust periodic solutions (…