Bird (mathematical artwork)

Short description: Mathematical artwork

A version of A Bird in Flight made up of 500 line segments Another version of A Bird in Flight made up of 20,001 circles

Bird, also known as A Bird in Flight refers to bird-like mathematical artworks that are introduced by mathematical equations.[1][2][3][4][5][6][7] A group of these figures are created by combing through tens of thousands of computer-generated images. They are usually defined by trigonometric functions.[8][9][10][11][12] An example of A Bird in Flight is made up of 500 segments defined in a Cartesian plane where for each k=1,2,3,…,500 the endpoints of the k-th line segment are:

(32sin7(2πk500+π3),14cos2(6πk500))

and

(15sin⁡(6πk500+π5),−23sin2(2πk500−π3)).

The 500 line segments defined above together form a shape in the Cartesian plane that resembles a bird with open wings. Looking at the line segments on the wings of the bird causes an optical illusion and may trick the viewer into thinking that the segments are curved lines. Therefore, the shape can also be considered as an optical artwork.[13][14][15][16][17] Another version of A Bird in Flight was defined as the union of all of the circles with center (A(k),B(k)) and radius R(k), where k=−10000,−9999,…,9999,10000, and

A(k)=3k20000+sin⁡(π2(k10000)7)cos6(41πk10000)+14cos16(41πk10000)cos12(πk20000)sin⁡(6πk10000),
B(k)=−cos⁡(π2(k10000)7)(1+32cos6(πk20000)cos6(3πk20000))cos6(41πk10000)+12cos10(3πk100000)cos10(9πk100000)cos10(18πk100000),
R(k)=150+110sin2(41πk10000)sin2(9πk100000)+120cos2(41πk10000)cos10(πk20000).

The set of the 20,001 circles defined above form a subset of the plane that resembles a flying bird. Although this version's equations are a lot more complicated than the version made of 500 segments, it has a better resemblance to a real flying bird. [18][19]

## References

1. ↑ "Von Formeln und Vögeln" (in German). Spektrum der Wissenschaft 05/2021: 47. February 4, 2021. ISSN 0170-2971. https://www.spektrum.de/kolumne/freistetters-formelwelt-von-formeln-und-voegeln/1826563. Retrieved 9 April 2022.
2. ↑ "Mathematical Concepts Illustrated by ...". American Mathematical Society. November 2014. http://www.ams.org/publicoutreach/math-imagery/yeganeh.
3. ↑ .blog.gustavus.edu/2015/09/18/mathematical-works-of-art/ "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. https://mcs .blog.gustavus.edu/2015/09/18/mathematical-works-of-art/.
4. ↑ "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. https://plus.maths.org/content/not-bird.
5. ↑ Cavanagh, Peter (March 5, 2021). Avian Arithmetic: The mathematics of bird flight (Speech). National Museum of Mathematics' Events. MoMath Online, NY, United States. Retrieved April 3, 2022.
6. ↑ Gustlin, Deborah (17 November 2019). "15.4: Digital Art". https://human.libretexts.org/Courses/ASCCC/A_World_Perspective_of_Art_Appreciation_(Gustlin_and_Gustlin)/15:_The_New_Millennium_(2000_-_2020)/15.04:_Digital_Art.
7. ↑ "Mathematics Portal - IMKT". International Mathematical Knowledge Trust. https://imkt.org/math-portal/.
8. ↑ Antonick, Gary (January 25, 2016). "Round Robin". The New York Times. https://wordplay.blogs.nytimes.com/2016/01/25/moriconi-round-robin/.
9. ↑ Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN. http://edition.cnn.com/2015/09/17/arts/math-art/.
10. ↑ Baugher, Janée J. (2020). The Ekphrastic Writer: Creating Art-Influenced Poetry, Fiction and Nonfiction. McFarland and Company, Inc., Publishers. p. 56. ISBN 9781476639611. https://mcfarlandbooks.com/product/the-ekphrastic-writer/.
11. ↑ ""A Bird in Flight (2015),"". American Mathematical Society. September 16, 2015. http://www.ams.org/mathimagery/displayimage.php?album=40&pid=616#top_display_media.
12. ↑ Young, Lauren (January 19, 2016). "Math Is Beautiful". Science Friday. http://www.sciencefriday.com/articles/math-is-beautiful/.
13. ↑ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog). http://blogs.scientificamerican.com/symbiartic/mathematically-precise-crosshatching/.
14. ↑ "เมื่อคณิตศาสตร์ถูกสร้างเป็นภาพศิลปะ" (in th). Chulalongkorn University. https://www.faa.chula.ac.th/SelfLearningFaamai/detailform/119.
15. ↑ Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog). http://blogs.scientificamerican.com/symbiartic/mathematically-precise-crosshatching/.
16. ↑ ""A Bird in Flight (2016),"". American Mathematical Society. March 23, 2016. http://www.ams.org/mathimagery/displayimage.php?album=40&pid=684#top_display_media.
17. ↑ Passaro, Davide. "Matematica e arti visive: percorsi interdisciplinari fra matematica, arte e coding". SIMAI Società Italiana di Matematica Applicata e Industriale. http://maddmaths.simai.eu/archimede/matematica-e-arti-visive/.
18. ↑ ""A Bird in Flight"". April 22, 2018. https://www.futilitycloset.com/2018/04/22/a-bird-in-flight/.
19. ↑ "수학적 아름다움, 프랙털 아트의 세계" (in ko). Sciencetimes. 8 December 2020. https://www.sciencetimes.co.kr/news/수학적-아름다움-프랙털-아트의-세계/.

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