Joining up the dots

This is used to illustrate the issue of retrospective coherence in complexity

Number of Dots	Number of Links ${\frac {n(n-1)}{2}}$	Number of Possible Patterns $2^{\frac {n(n-1)}{2}}$
4	6	64
10	45	35,184,372,088,832 or 35.2 trillion
12	66	73,786,976,294,838,200,000 or 73.8 quintillion