English: The horizontal and vertical axes indicate the initial angles θ₁ and θ₂ of a compound double pendulum, ranging from ${\displaystyle (-\pi ,-\pi )}$ in the lower left corner to ${\displaystyle (\pi ,\pi )}$ in the upper right corner. Points are colored according to the w:Lyapunov exponent of the double pendulum with those initial angles and zero initial momenta, calculated via regression on points sampled from simulation of two pendulums with initial conditions differing by less than one thousandth of the pixel image's pixel resolution. The lowest Lyapunov exponent visible in the image, shown in dark blue, is approximately -0.0466. The highest, shown in dark red, is approximately 0.2979. All colors are given by the Turbo rainbow color map. Values are given at time scale of ${\displaystyle {\sqrt {l/g}}}$. Simulation was performed on a 12000×12000 grid of double-width floating point numbers with 8th order Dormand–Prince and GPU acceleration for 100 units of time.