Can't tell if I made a chaotic circuit or if I broke the sim

[ibuildstuff]

So, I was playing around with a couple of voltage multiplier circuits a few months ago, and while optimizing one design, I came up with a pretty neat (not to brag) way of converting a sine wave to a square wave by using transformers in a completely different way than normally. A little while ago, I got bored and decided to test it in some free online simulator I found. Surprisingly, it seemed to work perfectly. Even more surprisingly, after playing around with it for a while, I was able to observe some pretty surprising effects.

Here's the circuit diagram, as best as I can remember it. It's pretty simple, but if you probe the voltage difference between points 1 and 2, you'll see a very odd periodic pattern: a sine wave for half of the period, followed by rapid, chaotic oscillations for the other half, if I remember correctly. Measure 3 and 4 to see the square wave:

If you're using a simulator, you may have to wire it like this (I don't remember why. Something about the direction the current is traveling or something):

So, is this truly chaotic behavior? Also, I'm sure everyone will agree with me when I say inductors are weird, but I still can't figure out why this circuit would behave so erratically. Any ideas?

 

[Baluncore]

Your unusual circuit is duplicated. You only need to simulate half at the time.
That way you will be able to ground your AC supply and your resistive load.
Are you deliberately saturating the transformer cores or are you trying to alternate the flux direction ?

The magnetic saturation of transformer cores is used to control power.
http://en.wikipedia.org/wiki/Saturable_reactor
http://en.wikipedia.org/wiki/Royer_oscillator