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Saturation

The final conceptualization is that of saturation, introduced by Christopher Westland. Imagine a porous material on which water is poured. In the material, which can be modelled as a two dimensional grid, there are a limited number of random connections between its cells. Using something called perlocation theory it can be calculated that only when connections occur with a probability of 50% in such a material, a pathway will be formed, and the water will be able to run out at the bottom.

Now if we see an application (say a social networking application) as forming the pathway between the points, we can say that inside it a so called giant cluster (pathway connecting most users) appears when it connects 50% of its target population (the cells). At this point critical mass is attained. Before this happens, there will be many small separate clusters. So that when people receive invites from their friends, they only receive invites from a few of them, which is not enough to cause them to sign up.

Regardless of its mathematical rigour, this conceptualization does not apply well to hypertext applications. As both invites and a monolithic cluster connecting all users, are not central to them. Thus it is not considered further in this essay. We will mostly be working with the first two minimalistic conceptions of critical mass: a threshold and the minimum size of the core-group of active users required.

\section{Thresholds}

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