>>53
Better define the term ``strand''. Also, it depends on the
dimension of the cycle.
For a cycle of large dimension, probably more than 50% of the elements are part of the cycle. For a cycle of dimension 10, there's probably only a very small percentage of elements that are part of the cycle. Much less than 1%, I'd say.
Here I define cycle of dimension
2 to be
f(f(x)). A cycle of dimension
1 would just be
x = f(x).
Also, if the hash has collisions, the number of "unreachable" outputs is the same as the number of collisions. Obviously because if it outputs
n hashes, and
x of those hashes are the same, the number of different hashes is
n - x, which leaves
n ``holes''. Assuming the input and output space are the same.
You might want to look into linear regression for the statistical approach in finding these quines.