[Haskell-cafe] Re: About Fibonacci again...
Mirko Rahn
rahn at ira.uka.de
Thu Nov 8 04:01:40 EST 2007
> 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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