This Demonstration shows the path of a point mass falling through a Galton board under the influence of gravity and air friction. The nails that deflect the point mass are modeled to have a finite radius and a soft, rubberÃ¢ÂÂlike surface material. The detailed path of the point mass depends sensitively on the initial conditions.
Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica GuideBook for Numerics, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA
For theoretical results on flows through Galton boards, see:
L. Bruno, A. Calvo, I. Ippolito, "Dispersive Flow of Disks through a Two-Dimensional Galton Board," Eur. Phys. J. E, 11(2), 2003 pp. 131-140.
N. Chernov, D. Dolgopyat, "Diffusive Motion and Recurrence on an Idealized Galton Board," Phys. Rev. Lett., 99(3), 030601, 2007.
For the influence of the operators on the paths, see:
R. G. Jahn, B. J. Dunne, "On the Quantum Mechanics of Consciousness, with Application to Anomalous Phenomena," Found. Phys., 16(8), 1986 pp. 721-772.
B. J. Dunne, R. D. Nelson, and R. G. Jahn, "Operator-Related Anomalies in a Random Mechanical Cascade," J. Sc. Explor., 2(2), 1988 pp. 155-179.