Mechanical Pendulums vs 4Dice

In mechanics, in the area of dynamical system, a N-tuple pendulum is a set of N simple pendulums attached to each other. These N-tuple pendulums are physical systems that exibits rich dynamical behavior. For certain energies, are the motion of these mechanical pendulums often chaotic. You can influence the motion of the pendulums by holding your device in different positions. The equations of motions of these pendulums has been derived using the Sophia mechanical package. The different set of differential equations are solved using the 4:th order Runge-Kutta method for the time stepping. Within this application you can switch between these mechanical pendulums: - Double - Triple - Quadruple - Quintuple - Sextuple - Octuple - Symmtric Double - Simple 3-Dimensional The visualization of the pendulums can be viewed in either a Quartz view or in an OpenGL view.

This application exploits multitouch controls to explore a hypercube labeled as a 4-dimensional, 8-sided die. The hypercube's eight cube-shaped faces are rendered as a 4D being would see them in 4D light: thus, only one, two, three, or four cubic faces can appear at one time while the die rolls, but no more. Faces that would be invisible to a 4D gambler cannot be seen without interactively rolling the die to bring them into view.