This is an example of cellular automata. It is a rather simple, abstract form of urban modeling. In this case, I used Excel to calculate values (expressed as a cell height) for each cell on a 24 * 24 grid. This specific pattern emerged from the following conditions:

The starting condition was a perfectly even distribution over the 24*24 grid (value of each cell was 1). The basic idea here is that adjacency leads to growth (an oversimplified notion of agglomeration economies). Having cells directly next to you contributes more to growth than having cells diagonally away from you. (One could make this model even more interesting by also introducing diseconomies of scale -- that is, overcrowding leads to decline.)

In each step, the new value of the cell was calculated based on the following:
New Value of Cell =(0.4 * (own cell value) + 0.2 * (sum of side cell values) + 0.1 * (sum of cells on the corner of the cell)) * random factor)

The pattern below resulted after the 10th iteration. For more info on cellular automata for urban growth, use this google search link.