Turtle graphics of morphic streams
نویسنده
چکیده
Streams are infinite sequences. The simplest streams that are not ultimately periodic are morphic streams: fixed points of particular morphisms mapping single symbols to strings of symbols. A most basic way to visualize a stream is by a turtle curve: for every alphabet symbol fix an angle, and then proceed the stream elements by drawing unit segments and turn the corresponding angle. This paper investigates turtle curves of morphic streams. In particular, criteria are given for turtle curves being finite (consisting of finitely many segments), and for being fractal or self-similar: it contains an upscaled copy of itself. Also space filling turtle curves are considered, and a turtle curve that is dense in the plane. As a particular result we give an exact relationship between the Koch curve and a turtle curve for the Thue-Morse stream, where until now for such a result only approximations were known.
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