Flashing light when pushing bike with (constant) low speed When someone pushes his bike beside him in a constant (low) speed the light will not be at constant (low) brightness, instead it will flash with it's full brightness. 

Why does it work like that?
This happens because the power from a hub dynamo (which technically is a magneto, not a true dynamo) is not clean sine-wave AC but consists of short pulses with alternating polarity. At high speeds these pulses follow each other fast enough that a LED can burn continuously with a small capacitor and a filament bulb does not have time to cool down between pulses.

The effect does not have anything to do with programming or the fact that LED is a diode, and it happens with filament bulbs too. A more complex LED setup could have a capacitor to enable continuous dim light and perhaps even be programmed to flash at low input power, but I doubt this is the case.