Image: A Bird in Flight by Hamid Naderi Yeganeh 2016

Description: A Bird in Flight by mathematical artist Hamid Naderi Yeganeh. This image shows all circles of the form: (x−A(k))2+(y−B(k))2=(R(k))2{\displaystyle (x-A(k))^{2}+(y-B(k))^{2}=(R(k))^{2}}, for k=−10000,−9999,...,9999,10000{\displaystyle k=-10000,-9999,...,9999,10000}, where A(k)=(3k20000)+sin⁡((π2)(k10000)7)(cos⁡(41πk10000))6+(14)(cos⁡(41πk10000))16(cos⁡(πk20000))12sin⁡(6πk10000),{\displaystyle A(k)=\left({\frac {3k}{20000}}\right)+\sin \left(\left({\frac {\pi }{2}}\right)\left({\frac {k}{10000}}\right)^{7}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{6}+\left({\frac {1}{4}}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{16}\left(\cos \left({\frac {\pi k}{20000}}\right)\right)^{12}\sin \left({\frac {6\pi k}{10000}}\right),} B(k)=−cos⁡((π2)(k10000)7)(1+(32)(cos⁡(πk20000)cos⁡(3πk20000))6)(cos⁡(41πk10000))6+(12)(cos⁡(3πk100000)cos⁡(9πk100000)cos⁡(18πk100000))10,{\displaystyle B(k)=-\cos \left(\left({\frac {\pi }{2}}\right)\left({\frac {k}{10000}}\right)^{7}\right)\left(1+\left({\frac {3}{2}}\right)\left(\cos \left({\frac {\pi k}{20000}}\right)\cos \left({\frac {3\pi k}{20000}}\right)\right)^{6}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{6}+\left({\frac {1}{2}}\right)\left(\cos \left({\frac {3\pi k}{100000}}\right)\cos \left({\frac {9\pi k}{100000}}\right)\cos \left({\frac {18\pi k}{100000}}\right)\right)^{10},} R(k)=(150)+(110)(sin⁡(41πk10000)sin⁡(9πk100000))2+(120)(cos⁡(41πk10000))2(cos⁡(πk20000))10.{\displaystyle R(k)=\left({\frac {1}{50}}\right)+\left({\frac {1}{10}}\right)\left(\sin \left({\frac {41\pi k}{10000}}\right)\sin \left({\frac {9\pi k}{100000}}\right)\right)^{2}+\left({\frac {1}{20}}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{2}\left(\cos \left({\frac {\pi k}{20000}}\right)\right)^{10}.} See more details at: www.ams.org/mathimagery/displayimage.php?album=40&pid=684#top_display_media
Title: A Bird in Flight by Hamid Naderi Yeganeh 2016
Credit: https://archive.org/details/A_Bird_in_Flight_Hamid_Naderi_Yeganeh
Author: Hamid Naderi Yeganeh
Usage Terms: Creative Commons Attribution-Share Alike 4.0
License: CC BY-SA 4.0
License Link: https://creativecommons.org/licenses/by-sa/4.0
Attribution Required?: Yes