Islands of Dirtiness

For the majority of this talk, we assume that the placement of objects is entirely random. Thinking back, this assumption is partially flawed. While it is true that most object can be randomly distributed throughout a room, in most cases, objects are left in very particular areas that I will call an Island of dirtiness. Consider clothes for example. While it is true that clothes may go anywhere inside a room, in many cases, people naturally gather all the dirty clothes and put them in a single pile. In another example, dirty dishes, while it is true that dirty dishes may be place anywhere throughout a house, they tend to be left only in certain areas where either dirty dishes are cleaned or where food is eaten. Throughout a common household, there are numerous examples of said Islands of dirtiness. Outside of these islands, the area is relatively tidy, inside these islands however, there area may start to resemble the random nature of the ping-pong problem discussed in the first section.