We will explore a discrete model for the formulation of lightning. We place randomly generated numbers (levels) in each cell of an m x n grid, creating a configuration. Choosing a starting cell along the top row, we examine the neighboring cells and (i) draw an edge to any neighbor whose level is less than or equal to our current level (such a cell has become visited), (ii) list the visited cells in a queue, and (iii) start the process over at the beginning of the queue, proceeding until the queue is empty. We are interested in the fate of the resulting path, and would especially like to be able to compute the probability that some portion of the path reaches the bottom of the grid. We think of this case as success, or more colloquially, a lightning strike. This is joint work with Lauren Sobral, a U of M undergraduate.

Thackeray 703