8 Nov
2007
8 Nov
'07
4:01 a.m.
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