Figure 1
Merging Wada basins. The time-2π (Poincaré) map of the forced damped pendulum defined by \(\ddot{x}+0.2\dot{x}+\,\sin \,x=1.66\,\cos \,t\) possesses three attractors, and consequently its phase space \((x,\dot{x})\) contains three basins. This system verifies the Wada property4. (a) The top-left panel (in red, green and blue) represents the Wada basins, where one color corresponds to one basin. The other three panels are the result of the action of merging the basins: we merge two colors, and keep the third unchanged. (b) In the top-left panel a disk is divided in three colors. The other three panels show the action of merging in this non-Wada picture. (c) The color-code of the merged basins can be inferred from the bottom-right picture: yellow = red + green, magenta = blue + red, cyan = blue + green.
