Description
A curlicue is a piecewise linear curve in the complex plane which can be generated by an arbitrary sequence of real numbers u_n. It can be interpreted as a trajectory of a particle in the plane which starts in the origin at time t=0 and moves with a constant velocity, changing its direction at instances t=0,1,2,3,..., where the new direction is given by a number 2*pi u_t mod 2*pi. In particular, when the sequence u_n is given by iterates of some dynamical system (e.g. a circle homeomorphism) at a given point we speak about dynamically generated curlicues. This dataset contains source codes of the Matlab functions Rotation.m, Arnold.m and Sequence.m which can be used to plot the first N points of a curlicue generated, respectively, by rotation on the circle by arbitary angle, the Arnold circle map (with different parameters) and the u_n=nlog(n). Additionally, these functions allow us to calculate other properties of a curlicue, such as corresponding Birkhoff average and diameter of a curlicue. Description of the functions and variables involved is provided as comments in mfiles. It's worth pointing out that the function Sequence.m can be easily modified to compute and draw a curlicue generated by an arbitrary sequence u_n given by explicit formula. We also include txtfiles with exemplary data obtained by these functions and four figures (epsfiles) generated by a function Sequence.m for various sequences. More details and precise definition of a curlicue is available in the file Curlicues_description, contained in the dataset and references therein
Dataset file
Details
 Year of publication:
 2020
 Dataset language:
 English
 Fields of science:

 Mathematics (Natural sciences)
 License:

CC BYAttribution
 DOI:
 10.34808/anjgq802 open in new tab
 Verified by:
 Gdańsk University of Technology
Keywords
Authors
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