Click on any applet to display animation.


Applet 1: Simulation of the entwined path and density of a single electron (see text) is shown in blue (forward time) and red (reverse time).  The horizontal axis is the x-coordinate of the entwined path (left) and the magnitude of the density (right).  The vertical axis is time for both graphs.



Applet 2: Simulation of the entwined paths and combined density of two electrons, out of phase by a quarter-period.  Two such electrons are called a fiber.



Applet 3: Simulation of the entwined paths and combined density of two fibers. One fiber is shifted by a half-period plus epsilon relative to the other fiber.  This arrangement of two fibers (four electrons) is called a cord.



Applet 4: Simulation of a cord (as in Applet 3) except that forward and reverse densities are added simultaneously.


Applet 5: A sine wave is shaped from many cords (see text).  In this simulation, N=10, meaning that there are 10 positions for delta functions in a half period.  At each position there are enough delta functions to shape the sine wave.



Applet 6:  The smoothness of the sine wave generated in Applet 5 can be improved arbitrarily by increasing N.  In this example, N=100 and only the density is shown.



Applet 7: An entwined path with a stochastic first cycle (see text).  Subsequent cycles are deterministic.



Applet 8: An entwined path with a stochastic first cycle and its density.



Applet 9: Two entwined paths with stochastic first cycles and the resulting density.


Applet 10: Thirty entwined paths with stochastic first cycles and the resulting density.


Applet 11: The density resulting from 10,000 entwined paths (with stochastic first cycles) is sinusoidal.