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The definition of an exactly self replicating function seems to be any function 'f' such that there are continuous bijections a,b,c such that f∘a + f∘b = c∘f, a
by contravariant 9y ago
The definition of an exactly self replicating function seems to be any function 'f' such that there are continuous bijections a,b,c such that f∘a + f∘b = c∘f, and a does not equal b.
Edit: I think this includes all strictly quasi-concave functions, but I'm not entirely sure.
- tylerneylon 9y agoI think you're right. Your version of the definition is more elegantly stated, and I may want to use it going forward, as long as a, b, and c still make intuitive sense (thinking about that part).
- contravariant 9y agoFeel free to use it. Using your notation you have a=t1, b=t1∘s, c=t2^-1. Inversely you have s=a^-1∘b, t1=a, t2=c^-1.