In a confined environment the growth rate of a population may not remain constant. In a lake, for example, there is some maximum sustainable population of fish, also called a carrying capacity. In this section, we will develop a model that contains a carrying capacity term, and use it to predict growth under constraints.  Because resources are typically limited in systems, these types of models are much more common than linear or geometric growth.

The famous Mandelbrot set, a fractal whose growth is constrained.