The Rabbit Sequence:
1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,...
This nasty acquaintance of mine asked the students to write down a simple
procedure which generates the sequence after the infinite number of units
of time. Of course, any finite prefix of it.
In terms of limits of morphisms we can simply write
limit h w = l
where l = f w ++ f (tail l)
f = concatMap ((!!) h)
rabbit = limit [[1],[1,0]] [1]
Some other well known sequences:
fibonacci = limit [[0,1],[0]] [0]
thue_morse = limit [[0,1],[1,0]] [0]
cubic_free = limit [[0,1,2],[0,2],[1]] [0]
Of course, we have
map (1-) rabbit == fibonacci
/BR
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