Flashing light when pushing bike with (constant) low speed
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.