This concept is the metaphoric use of the Law of Thermodynamics. There is a force that initiates the motion of objects, accelerates it and eventually the motion decays. The later phrase is called entropy. In the same manner if the energy or force applied for acceleration or maintenance becomes beyond the capacity of the ‘engine’, then it has to slow down or break down. If it is desired that the engine be able to function with additional energy applied then the engine must be adapted for this. However there are still limitations. These limits are fuzzy, but at some point there is definite moment of transition.
As an adjunct to this concept of the Law of Thermodynamics is that of a filter that changes the rules for fractal generation. For example, an already established city has set-up a policy of protection of a watershed in an area on the edges of urban development. This will determine the formation of urban fractals within the watershed protection area. It may mean that the some urban development already growing in the direction will have to go somewhere other than the area (i.e., heavy industry) or the residential, commercial or industrial development has to be altered to minimize pollution to the watershed. The development will grow, fill up the space and eventually become stable, but depending on a ‘filter’ that altered the fractal formation.
These brief paragraphs are fragments of thoughts about the application of the Law of Thermodynamic to fractal generation. They should be expanded upon at a later date. Any comment or criticism is welcomed