منابع مشابه
Turtle graphics of morphic streams
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...
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Motivated by striking properties of the well known Fibonacci word we consider pictures which are defined by this word and its variants via so-called turtle graphics. Such a picture can be bounded or unbounded. We characterize when the picture defined by not only the Fibonacci recurrence, but also by a general recurrence formula, is bounded, the characterization being computable.
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This note is a response to one of the problems posed by Kwa´sniewski in [1, 2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence F is at the point product of primary GCD-morphic sequences and any GCD-morphic sequence is encoded by natural number valued sequence satisfying condition (C1). The problem of general importance-for example in number theory was formulate...
متن کاملA Taxonomy of Morphic Sequences
In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no example is possible.
متن کاملOn Uniformly Recurrent Morphic Sequences
In the paper we mainly deal with two well-known types of in nite words: morphic and uniformly recurrent (=almost periodic). We discuss the problem of nding criterion of uniform recurrence for morphic sequences and give e ective polynomial-time such criterion in two particular cases: pure morphic sequences and automatic sequences. We also prove that factor complexity of arbitrary uniformly recur...
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ژورنال
عنوان ژورنال: Fractals
سال: 2016
ISSN: 0218-348X,1793-6543
DOI: 10.1142/s0218348x16500092