Chaotic dynamics of a ski slope with a magnetic mogul field

The game of Plinko, as seen on the CBS television show The Price Is Right, demonstrates rich chaotic dynamics as evidenced by a strong sensitivity to initial conditions. This behavior can be readily observed by watching repeated runs of the Plinko puck and noting the final location of the puck once it has passed through the peg lattice: despite the fact that many runs often start nearly co-located, the runs will often take very different paths and the puck will find its way to a seemingly random final position. This observation leads us to believe that the system is indeed chaotic, exhibiting behavior similar to that of a pinball machine with dissipation or a vertical billiards table. A review of the literature on these topics quickly reveals that the pinball machine offers rich chaotic dynamics when combined with a collision rule that adds energy into the system (despite conventional notions that only dissipative systems show the presence of attracting behavior and phase space contraction) and that pinball billiards shows equally ordered chaotic behavior when paired with a dissipative (non-elastic) collision rule and modified boundary properties. These reviews led to the assumption that the chaotic behavior of the analogous systems would generalize well to the Plinko problem and that this would enable the discovery and mapping of basins of attraction and strange attractors within the system under study. This paper discusses the issues with modeling Plinko and introduces an analogous model that was created from attempting to solve the problems related to Plinko’s dynamics. This analog model was studied in place of the real Plinko system, and it’s behavior compared to that of a closely related pedagogical example: ski slope chaos.