I'm reading my electronics handbook, RS# 62-5004, pages 50 and 113.
the flasher in the book is very similar to the one i've posted, except it uses PNP transistors on the positive end, upposed to the NPN shown on the negative end of the circuit.
in a schematic, the line side of an LED is the cathode (connect to ground) side and triangle is Anode (positive) side. On the transistor, the arrow points the direction of flow (Collector to Emitter for NPN; Emitter to Collector on PNP).
In the circuit shown, the positive charge goes from the source to the anode side of both LEDs, through the resistors, to the collector of the transistors.
Also, it goes though the high resistance resistors, down to the base of the transistors.
Meanwhile, it also goes into the storage capacitors
Now, the logic part (i'm gonna go left to right)-
As the electricity goes through the (left) LED's and resistors, the power has to go into the (left) capacitor because the transistor is closed. Since the (right) resistor is high, the power takes the easiest path- being stored in the capacitor. But since there has to be a complete circuit, while the capacitor is building voltage, there is a slight energy amount going into the base of the (right) transistor, allowing it to be powered on. This allows the electricity to flow through the (right) LED and resistor, through the transistor, and won to ground, making that side light up.
Yes, it's confusing, even to me. But it works. What makes it switch sides is that while one LED is on, the capacitor for the opposite side is charging. The power source never actually goes directly to the LED, the capacitors power them.