[ineptech]

Eh, the coins weren't important, that's just an easy thing for me to visualize. If one graphs that emergence -if one graphs the number of nodes in a graph against the chance of finding some structure in a graph of that size - I had imagined one would see a smooth curve like one half of a binomial distribution curve. It sounds like you're saying the graph would look discontinuous?

[lupire]

It's as continuous a want discrete function can be, but yes it has a region of explosive growth, sort of like a sigmoid.

Think of all the Jenga games. What is the probability of the tower collapsing on turn T (or T/H, for a tower of size H), graphed as a function of T (or T/H)?