English: This image is an update of this chart (File:Double_pendulum_flips_graph.png). In higher resolution an a different color scheme.

Explanation: The x and y directions represents the angles that a double pendulum consisting of two uniform bars of same length and mass makes with the vertical direction, being the center of the image 0º and the extremities +- 179.9º. Both bars are initially with zero velocity. The color represents the time (in units of ${\displaystyle {\sqrt {l/g}}}$) that it takes for one of the two pendulums to flip, being black less than 1 unit of time, from red to violet it ranges in a logarithm sacel from 1 to 10000 units of time. White means no flip was observed within 10000 units of time.

Calculations Details:

The calculations were done using an 8th order Runge-Kutta-Fehlberg embedded with a 7th order method. Tolerance was set to ${\displaystyle 10^{-10}}$ for the maximum absolute value of all four components of the phase space. To give an idea this resulted in an average time step of 0.025 units of time.