The answer to my question is an expression on the form x(2) = x(1) + x(0) but the indexes can be different.
But to give a meaning to that expression you also need to include the shortest bitstring that can be used to initialize the infinite bitstring.
As in the very simple example,
Bitstring: 1101 where [x(0) = 1, x(1) = 1, x(2) = 0, x(3) = 1]
The recursive function: x(2) = x(1) + x(0) gives
x(0) = 1
x(1) = 1
x(2) = (x(0) + x(1)) % 2 = (1 + 1) % 2 = 0
x(3) = (x(1) + x(2)) % 2 = (1 + 0) % 2 = 1
x(4) = (x(2) + x(3)) % 2 = (0 + 1) % 2 = 1
x(5) = (x(3) + x(4)) % 2 = (1 + 1) % 2 = 0
x(6) = (x(4) + x(5)) % 2 = (1 + 0) % 2 = 1
x(7) = (x(5) + x(6)) % 2 = (0 + 1) % 2 = 1
x(8) = (x(6) + x(7)) % 2 = (1 + 1) % 2 = 0
Which would produce the bitstring: 110 110 110 110 ...
This post has been edited by Gloin: 11 April 2009 - 05:49 PM

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