Over the course of experimenting with the Joule Thief circuit, It's come to my attention that, after having done some research, there may be more than one thread needing dedication to understanding the way the Joule Thief works in order to have a component level understanding of what is going on in the circuit.  ( At least for other people's sakes )

I've personally built seven or eight different circuits in the last week alone, and while none of them are the same, they all work.  So I've started this thread to focus on Blocking Oscillators specifically, because after observations, there seems to be many setups that work.

A blocking oscillator is the minimal configuration needed to create a free running signal ( usually a transformer with two or more windings, a capacitor, and a transistor ) - the device configuration garnering its name from the fact that it's turned off for most of the duty cycle... but as one can imagine, this could be more or less accurate depending on the configuration.

More information can be found here - it's short, but makes a point: http://en.wikipedia.org/wiki/Blocking_oscillator

Below are images of my various Joule Thief circuits which incorporate different types of blocking oscillator transformer configurations ( multiforms ) - all of which work.

I welcome you to post your windings here - they seem to be relevant elsewhere here in the forum.

( in order )
jt_attempt_8.jpg is a linear transformer consisting of two equal lengths of same gages wire twisted tighly around one another.  The interesting part of this one is that, given the circuit configuration, the LED will flash - slower if the capacitor attached to the blocking oscillator is higher, and if it is lower, it will speed up to the point of being continuously on - and then not at all if the capacitance is too small.
jt_attempt_7.jpg is a the simplest form, with there being less current carrying winding than voltage collecting windings.  Note that this particular setup has to be activated by bridging the positive battery terminal with the positive lead of the LED.  Also, an interesting aspect of this circuit is that after a while it will turn off - there's oscilations I suppose that cuase it to eventually run out of 'steam'.
jt_attempt_4.jpg and jt_attempt_3.jpg are essentially wire type inversions of one another.  Where current is carried through the internal coil while voltage is collected across the outter coil.  This toroid type is formed by the current carrying loop while the voltage  collecting coil is wrapped around the current carrying coil.