Akula0083 30 Watt Self Running Generator.

[verpies]

Please explain; I am one of those who doesn't get how the current can travel both ways through the diode.
http://makeagif.com/mqXzyk

Because in this ideal circuit the electric current does not travel in both directions through the diode. 
See this animation - it is more accurate.  The upper trace shows the current flowing through the diode and the lower trace shows the voltage across the capacitor.

In the real word, diodes can conduct electric current backwards, due to:
1) junction capacitance (see this)
2) finite reverse recovery time
3) reverse Zener breakdown.
4) reverse avalanche breakdown
5) the SRD effect.
6) reverse bias leakage current (insignificant)
7) reverse photocurrent

[Dave45]

See this animation - it is more accurate

Im sorry but no its not, it doesnt explain femf or bemf.

In the gif I showed the bemf from the coil hitting the leg of the capacitor, this leg then becomes pos.
Look at the schematic of the gif the neg of the battery is connected to the first leg the pos bemf hits the other leg this charges the cap.....pos on one side neg on the other.

If you run this pos bemf into another coil as Akula did its bemf will have a neg charge

Opposites attract, when a coil is hit with a neg pulse it takes on a neg charge as a whole, pos ions will form around the coil then when the magnetic field collapses it will bring a pos charge into the coil.

The same is true if you hit a coil with a pos pulse (as in the pos bemf from the neg charged coil) it takes on a pos charge and neg ions will form around this coil and its bemf or collapsing magnetic field will bring a neg charge into the coil.

[Dave45]

In the sim at falstad click options then uncheck conventional view and you will see how current truly moves through the circuit but it still does not show the coil reactions.

By looking at the circuit in the conventional view it appears the current continues in its original direction it appears as though whats truly bemf is femf and you see no polarity change as it moves through the diode.

[Dave45]

Welcome to the world of unconventional thinking and free energy. (pun intended) 
Oh did I mention I have a PHD, yea Im a post hole digger from way back.
roflmao
put a little joy in your heart
laughter is food for the soul

dave

[TinselKoala]

Dave, in your Falstead sim can you put scope testpoints right at both ends of the coils, and watch the voltage traces there as a pulse happens?