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Abstract:
Abstract: This study extends dynamic pattern approach to
cyclic drawing of planar geometrical patterns (viewed as end-point
movements) from smooth to piece-wise trajectories. Experimental
data on cyclic continuous drawing of dash, circle, and square are
analyzed for patterns of timing and coordination. The abrupt cyclic
frequency transitions as well as specific patterns of symmetry
breaking were found in the movement trajectories. The patterns are
compared to analytically-derived constraints and to the patterns
obtained via computer simulation. It is shown that (1) the system
of two nonlinearly coupling oscillators mathematically similar to
that considered by Haken-Kelso-Bunz (1985) is able to produce
piece-wise closed trajectory and square- shaped trajectory in
particular, given appropriate symmetry of coupling term; (2) if the
system has multiple attractors of different symmetry it is able to
simulate both frequency transitions and trajectory symmetry
breakdowns observed in the experimental data; (3) analysis of
energy balance of the system allows to explain and predict maximal
tempo of particular pattern drawing given its mean-square amplitude
and level of trajectory distortion.
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