# Janko Gravner

AMS Math Reviews

Web Page: http://www.math.ucdavis.edu/~gravner/

Email: gravner@math.ucdavis.edu

Office: MSB 3210

Phone: 530-752-0825

### Research

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 largeâ€“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).

*Last updated: 2012-05-08*