|Wesley R. Elsberry
Joined: May 2002
Here's an interesting graph:
I've put a 20 pixel border around this. On the X axis, there is the number of correct letters (treated as a continuous scale), and mutation rate is on the Y axis. I've taken terms from the "expected number of correct letters in a mutated string" calculation and subtracted the term for expected conversion of correct to incorrect from the expected conversion of incorrect to correct. Black is a net 28 expected new incorrect letters, white is a net 2 expected new correct letters, and the border color is where the two terms cancel each other out. One can see at a glance that as one considers candidates with more matching letters, only lower mutation rates are going to give a good chance of matching all the letters.
And here's the same graph, but with the net 1 expected new incorrect values shifted to black, too, making a contour visible, and showing how the mutation rate interacts with expectations for new candidate strings:
"You can't teach an old dogma new tricks." - Dorothy Parker