Experiment #1: A sine wave propagating through a 1 dimensional space with the transfer gain set at 2.0. The sine wave does not distort. Also switch to a square wave and restart the demonstration. The square wave does not distort.
This demonstrates that this is a viable mathematical model.
Experiment #2: Switch to a sine wave, set the gain to 1.0 and restart the demonstration. You will notice that the wavelength is shorter and that it grows or spreads as it travels. This, I believe is the cause of the Hubble constant. The universe is not necessarily expanding. The "apparent" Doppler shift is due to the nature of wave propagation itself.
Experiment #3: Switch to a square wave, set the gain to 1.99 and restart the demonstration. You will observe that the harmonics cannot travel as fast as the primary wavelength. The higher frequencies appear to fall behind. This is the same behavior observed in ocean waves where the velocity of the wave is proportional to the square root of the wavelength. Try the experiment again with the gain set to 0.5 (a very poor media).
The wave's velocity is related to the transfer gain.
vel = √ (gain/2.0)