Spreading Rumors

The spread of a rumor is an example of logistical or S-curve growth. Initially, only a small fraction of the population may know some rumor. These individuals pass the rumor on to their neighbors. The cycle repeats. Eventually, the number of people in the population who have heard the rumor grows exponentially. However, there are soon so many people who have heard the rumor that it becomes difficult to find someone who hasn't heard. The number of people hearing the rumor for the first time begins to level off creating an S-shaped curve.

models/Sociology/Rumor

In the rumor model patches represent people. A patch turns from black to red when it first hears the rumor. It then spreads the rumor to its four (or eight) neighbors. Of course these neighbors may have heard thee rumor already, possibly many times.

Turn off screen wrapping. Run the rumor model with setup-one. Watch the rumor spread.

Note the S-shaped rumor spread curve.

The successive differences curve plots the number of people hearing the rumor for the first time at each moment. Note that it is shapped like a jagged mountain.

The successive ratios curve plots the percentage of people hearing the rumor for the first time at a given moment.

Experiment with the times heard and when heard options.