>>101
Err, sorry. Mistake. The following:
where xi + ji = yi in Y.
Should be:
where (xi + ji) mod N = yi in Y.
>>102
I'm still not clear on what you mean by strands. Also, say that there
are collisions. This means that for an endpoint
x there is more than one way to get to it. So depending on the number of collisions and path of the hash, over time, many cycles will converge towards collisions, and if you had the time to compute the entire input space, you could use a large bit array to get a bit table of where all the "holes" are.
What is your assumption of the 1 cycle quine
f(0) = 0 based off of? Do you define a strand to be a cycle that doesn't connect to the rest of the set? Is that what you're saying? Maybe a better term would be string, then. Since even though it doesn't connect to the rest of the set, it'll loop in on itself many times.