Abstract
We present a study of the sensitivity of trajectories of pool balls to initial conditions. In the first component of the study our simulations include all sixteen balls. Variables include cue ball initial velocity and position on the “table”. We find that in a certain regime of initial conditions the system seems to show self-similarity, but as the range of initial cue ball angle and initial velocity is restricted, the system exhibits an interesting evolution towards a single point in parameter space, with the ball landing in only one pocket. We also examine the effects of varying the number of balls on the table, and how their dynamics may be interpreted using various plots and maps. Finally, the trajectory of a single cue ball is examined while it moves through the table space. Starting with the cue ball placed in the middle of the right wall of the table (traditional and rectangular in shape) and fired directly downward the system exhibits a two-cycle pattern. Then as the angle of fire is increased the system exhibits a four cycle, a three cycle and finally a two cycle all separated by noisy patterns. Effects of numerical artificialities are briefly discussed.
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