Curves formed by colonies of micro-organisms growing on a plane surface

In many cases, when a colony of micro-organisms such as moulds, yeasts or bacteria grows on the plane surface of a solid medium ( e.g. agar), starting from a single cell, the colony tends to grow as an ever expanding circle. The reason for this is that every cell, if free from competition, can multiply at roughly a constant rate in all directions in a plane, limited by the fact that territory occupied by one cell cannot be occupied by another. For the purposes of the present discussion, we can assume, as a first approximation, that the whole process is two-dimensional.