File:Bred vector growth rates in Lorenz system.png

English: The growth rates of bred vectors in the Lorenz system, defined as ${\displaystyle g={\frac {1}{n\Delta t}}\ln {\|\delta \mathbf {x} \|/\|\delta \mathbf {x} _{0}\|}}$, where ${\displaystyle n}$ is the number of time-steps in the breeding cycle, ${\displaystyle \Delta t}$ is the length of the time-step, ${\displaystyle \|\delta \mathbf {x} \|}$ is the magnitude of the bred vector after the cycle, and ${\displaystyle \|\delta \mathbf {x} _{0}\|}$ is its original magnitude. Blue indicates ${\displaystyle g<0}$, green indicates ${\displaystyle 0\leq g\leq 3.2}$, ${\displaystyle 3.2\leq g\leq 6.4}$, and red indicates ${\displaystyle 6.4\leq g}$