Basic aggregation model
This model appears to have first been described by Murray Eden in 1961 as a way of studying biological growth, and was simulated by him on a computer for clusters up to about 32,000 cells. By the mid-1980s clusters with a billion cells had been grown, and a very surprising slight anisotropy had been observed. The pictures below show which cells occur in more than 10% of 1000 randomly grown clusters. There is a 2% or so anisotropy that appears to remain essentially fixed for clusters above perhaps a million cells, tucking them in along the diagonal directions. The width of the region of roughness on the surface of each cluster varies with the radius of the cluster approximately like r1/3. The most extensive use of the model in practice has been for studying tumor growth: currently a typical tumor at detection contains about a billion cells, and it is important to predict what protrusions there will be that can break off and form additional tumors elsewhere.