Two profiles of force and cup and ball displacement exemplify unpredictable dynamics (left) and predictable dynamics (right).

<p>The strobing procedure is illustrated by the dots and the vertical lines: at every peak of the cup displacement, the value of force is picked; the strobed force values are then projected onto the vertical axis to show the distribution for each simulation. The left example shows a scattered distribution, while the right periodic profile only shows one value. The bifurcation diagram summarizes all force distributions as a function of the parameter , the initial ball angle. The vertical axis displays the stroboscopic samples of force values , simulated from a 1.0 Hz sinusoidal cup displacement with 10 cm (full peak-to-peak) amplitude and rad/s. The horizontal axis shows the initial ball angle . The plot shows that when the simulation starts from the initial angle = 1.0rad, the strobed force values do not change in successive cycles (blue), corresponding to the time profile on the right. At rad, there is variance in the strobed values of force , corresponding to the plot on the left (purple). The variance of was used to define a measure for the predictability of object's dynamics (see <i>Predictability Index</i> in the supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003900#pcbi.1003900.s003" target="_blank">Text S1</a>).