How to Model Unguided Evolution/ Natural Selection- an Idea
A good model of unguided evolution would be Dawkins' "weasel" without using the target sequence as a selection coefficient. Instead you would have to choose some arbitrary way of eliminating daughter sequences. Or you could just keep all daughter sequences to raise your odds- this is asexual reproduction after all.
Run that program and see how long before you get "Methinks it is like a weasel."