Professor Gravner studies deterministic and random cellular automata. These mathematical objects describe configurations which evolve by a repeated update of a local rule. Cellular automata have been used to model many natural phenomena and have offered insights into fundamental organizational principles in many scientific fields. From a more abstract perspective, cellular automata are a suitable tool used to characterize and catalog local dynamics which generate a prescribed global phenomenon. An important feature of this field is the interplay between rigorous mathematical analysis and large–scale computation, data analysis,and visualization.
Selected publications Gravner, J., and J. Quastel. "Internal DLA and the Stefan problem," Annals of Probability, 28(4):1528-1562, (2000), Full Text.
 Gravner, J., and D. Griffeath. "Random growth models with polygonal shapes," Annals of Probability, 34(1):181-218, (2006), Full Text.
 Gravner, J., Pitman, D., and S. Gavrilets. "Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities," Journal of Theoretical Biology, 248(4):627-645, (2007), Full Text.
 Gravner, J., and D. Griffeath. "Modeling snow-crystal growth: a three-dimensional approach," Physical Review E, 79: 011604, 1-18, (2009), Full Text.
 Gravner, J., and D. Griffeath. "Asymptotic densities for Packard Box rules," Nonlinearity, 22(8):1817-1846, (2009), Full Text.
Last updated: 2012-05-08