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Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions
- 1 Ulink College of Shanghai
* Author to whom correspondence should be addressed.
Abstract
Perfectly symmetric curves always have a high degree of aesthetic value. While it is difficult to draw them by hand, Spirograph is an old and popular drawing toy that produces fascinating symmetric patterns. In playing with drawing software, the author explores types of Spirograph patterns, the type identification method, and the parametric equations to express Spirograph mathematically. This paper also discusses the key parameters of a Spirograph pattern and how they affect the pattern’ shape. Finally, Spirograph pattern design is carried out by analyzing the features of a random pattern and estimating its different parameters. These results to some extent demystify and predict the seemingly infinite Spirograph patterns, as the corresponding parameters of a given Spirograph pattern can be found so that the similar image can be drawn by hand through a physical Spirograph set.
Keywords
spirograph, trochoid, rotation, parametric equation, parameters
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Cite this article
Li,W. (2023). Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions. Theoretical and Natural Science,10,64-78.
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Volume title: Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
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