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Re:The Ball-of-Mud Transition, or how software gets complex by gavinpc on Monday October 14, 2013 @01:36PM (#6548529)
This is very close to the "percolation problem." [0]

According to Robert Sedgewick, this particular problem has no known mathematical solution, and the threshold (for a given N) is only obtained through, e.g. a Monte Carlo simulations where you randomly open sites until the grid percolates (akin to the adding of threads). The whole thing is a good application of the union find algorithm.

The threshhold for N > 2 is about 60%. Not sure how that applies to software complexity, but it's interesting to think about.

Thanks, Coursera!

[0] http://en.wikipedia.org/wiki/Percolation_threshold

Re:The Ball-of-Mud Transition, or how software gets complex by joe_the_user on Monday October 14, 2013 @11:12PM (#6551279)
You mean one particular percolation problem, I assume.

Just to clarify because one might interpret your statement to mean that percolation problems in general don't have exact formulas for their solution but the "exact formula" section in your link would say otherwise.

Re:The Ball-of-Mud Transition, or how software gets complex by selimthegrim on Monday October 14, 2013 @03:41PM (#6549178)
For general graphs, the situation is indeed poor. For lattices, much more is understood, cf. http://en.wikipedia.org/wiki/Stanislav_Smirnov