The first task is to find an efficient way of writing the equations. 1 along the bottom and right. To determing the interior temperatures we solve a system of 400 equations in 400 unknowns. Since it is difficult to interpret a table of 400 numbers we represent the result graphically, coding the numerical temperature by a color between red and blue, where red is the hottest temperature and blue is the coldest. This kind of function models bacterial populations as long as the bacteria are not too crowded.
Growth is exponential, and quite rapid.
30,000,000,000 Such growth, illustrated in the figure below, cannot continue for long, so a more realistic model is needed. We will examine the model introduced by the Princeton biologist Robert May in his study of insect populations. One approach is to generate the sequence using a simple computer program , then graph the results. It is a fixed point of the function. For example, if we start above equilibrium, we have something like the graph below.