VCC = Voltage of the voltage source
VLED = adding all LED voltages
VBE = base/emitter voltage of a transistor
Current is constant until voltage VLED + (2 * VBE) reaches or exceeds VCC.
Tested in real with 2N2222 transistors and white LED with a blocking voltage of 2.95V. If voltage of the current source drops below 15V the current decreases.
The constant current (I) through the LED's is calculated by R = VBE / I.
In my real life example it was 630mV / 20mA = 31.5 Ohm. I used a 33 Ohm resistor and the current measured was 18mA.
I saw this circuit at the YouTube channel from Qualiflyer.