Unusual LED behavior

[InGaN]

I was using a nearly dead 3.6v phone battery connected to a white LED. Of course it lit up, but connecting a lower voltage LED (ie: green) shut it off (duh). But, when I disconnected the green LED, I was surprised to find the white one slowly came back on (kind of like a HID light). Keeping the green LED on longer before disconnecting it increased the time for the white to come on. I bet someone could design a circuit to do this, making white or blue LEDs "warm up" like HID, and placing them in your Bit or ZipZap.