This image shows the dynamical plane of (the complexification of) the circle map defined by f(x) = x + a + b*sin(2*pi(x))/(2*pi) (mod 1), where a=0.201 and b=2.864. This is an element of the so-called Arnold family, also known as the standard family, of circle maps - the simplest mathematical model of phase-locking phenomena. The function in question has two periodic attractors of period 4; their basins are shown in purple and red. (The components of the second basin are very small.) Points that do not eventually enter the unit circle under iteration are shown in grey, with different shades depending on how often the orbit maps inside / outside of the circle. This image was used in the exhibit "Dynamical Systems and Chaos: The Arnold Family" at the IMA@50 Festival of Mathematics and its Applications in Manchester, July 2014, illustrating recent research by Rempe-Gillen and van Strien.