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A Bird in Flight is the name of some bird-like geometric patterns that introduced by mathematical artist Hamid Naderi Yeganeh. Yeganeh has created these figures by combing through tens of thousands of computer-generated images. They are defined by trigonometric functions. An example of such patterns is a composed of 500 line segments where for each ${\displaystyle i=1,2,3,...,500}$ the endpoints of the ${\displaystyle i}$-th line segment are:

${\displaystyle \left({\frac {3}{2}}\left(\sin \left({\frac {2\pi i}{500}}+{\frac {\pi }{3}}\right)\right)^{7},\,{\frac {1}{4}}\left(\cos \left({\frac {6\pi i}{500}}\right)\right)^{2}\right)}$

and

${\displaystyle \left({\frac {1}{5}}\sin \left({\frac {6\pi i}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\left(\sin \left({\frac {2\pi i}{500}}-{\frac {\pi }{3}}\right)\right)^{2}\right)}$.

References

1. ""A Bird in Flight (2015)," by Hamid Naderi Yeganeh". American Mathematical Society. September 16, 2015. Retrieved September 19, 2015.
2. "Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. November 2014. Retrieved September 19, 2015.
3. "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved September 19, 2015.
4. Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
5. Naderi Yeganeh, Hamid (September 11, 2015). "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog).
6. Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).

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