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.
- Gravner, J., and J. Quastel. "Internal DLA and the Stefan problem," Annals of Probability, 28(4):1528-1562, (2000),
- Gravner, J., and D. Griffeath. "Random growth models with polygonal shapes," Annals of Probability, 34(1):181-218, (2006),
- 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),
- Gravner, J., and D. Griffeath. "Modeling snow-crystal growth: a three-dimensional approach," Physical Review E, 79: 011604, 1-18, (2009),
- Gravner, J., and D. Griffeath. "Asymptotic densities for Packard Box rules," Nonlinearity, 22(8):1817-1846, (2009).
Last updated: 2012-05-08