Viral Coefficients

Here's a cool chart I made awhile back to help understand "virality". Virality is defined as the expected number of children a user invites as a function of time (over a user's lifetime). The number of children a user is expected to spawn in on the t_th day can be modeled as V(t)=alpha*t^(n)and then this function is integrated up to T to get total invites up to that day. Below is a grid in which n and alpha are varied (n: -1.05 to -1.35 and alpha from 0.05 to 0.3). The chart shows the rate of acquisition of children in the first 7 days. There is also a V(7) and V(21) value below that and on the bottom is total expected number of children as T goes to infinity. The boxes are color coded by this total virality. It makes a good picture of the difference in total virality when the parameters, n and alpha, change slightly.