If we plot the logistic growth function, we receive a curve (called the
“sigmoid”) that is fairly similar to the curve we can see on the plot diagram
of our model (see Figure 9.3). Yet if we run the model repeatedly (with the
same parameter settings) we can see that the number of days needed for all
households to convert shows slightfluctuations. Further, the shape of the
plotted curve is not always entirely symmetrical. Finally, the logistic growth
function shows a faster growth (in less than 25 days). Why is that? For the
growth process to obey the logistic equation entirely, the agents would have
to be interacting completely randomly and homogenously, much like gas
molecules in a tank. In the model (as in the real world), however, encounters
and conversions do not take place in an entirely random fashion. Most
importantly, encounters between pagan households and believers are restrict-
ed to the perimeter of the group of already converted households, which form
an almost tight compact in the middle of the simulated world. This is not a bad
approximation of the growth of Christianity in the real world, which also grew
from a few important centers. It was certainly not the case that converted
households could access pagans in random parts of the Roman Empire (as the
logistic growth function would imply). Further, most of the times we run the
model, the movement will spread faster in some direction, resulting in regional
differences in the exposure of the remaining pagan households.^11 The physical
Followers0
0 5 10 15 20 255001000150020002500Days
Figure 9.3.The logistic growth function.small; thusFd×(1-Fd/N) will be small, as well. In this phase, the growth of the movement slows
down the speed of the growth.
(^11) On each day, NetLogo instructs households in random order to check if their neighbors are
followers. Due to this process, several households next to each other can be converted on the
198 Cognitive Science and the New Testament