The interactive visualization at the bottom of this page is based on "Threshold Models of Collective Behavior" (Granovetter 1978).
Granovetter describes collective behavior in which individuals each have a personal threshold. The threshold is the number of other people the individual needs to see partaking in the behavior before they will join in. This can cause cascading effects where huge numbers of people, even those who with very high thresholds, rapidly join in collective behaviors such as riots that they normally would not participate in.
The plot Granovetter uses to describe this is a cobweb plot, which plots iterative application of a function to an initial value.
The curve in Granovetter's fig. 1, which illustrates the interpretation of the cobweb plot, is not identified, but here is y = 3(x − 0.5)3 + 0.6, which is pretty close.
What the text describes in this section is not that curve but the CDF of the normal distribution, shown in the larger figure below. The normal distribution itself is plotted in the smaller figure. The plot is meant to relate the shape of the function to its behavior as a dynamical system. The line plotting the identity function F(x) = x is handy, since that is the function without behavior. The value of x decreases when the curve is below this line and increases when it is above it. The cobweb (animated below when x or σ is changed) shows the iteration. The new value is computed with the change represented by a vertical arrow. The horizontal arrow is drawn to the position of this value in the identity function, and then the process is repeated starting from the new system state.
The initial number of participants is given by x0 and σ is the standard deviation of the normal distribution.
Setting x0 to 0%, the cobweb shows how the number of participants changes with the iterative application of the rule, ending at a fixed point. At low values of σ the event cannot grow from a small number of participants to a large number, but as σ is increased, there is a sharp transition around σ = 0.12 where explosive growth becomes possible.