From its humble beginning 200 years ago our understanding and use of magnetism has come a long way. A short history lesson.
The telegraph sounder was basically a relay with no contacts. When power was applied it would click. When the power was removed it would clack. The time between the click clack would be long or short and would represent the characters in the message.
click-----clack---------------click----------clack would be the letter A. Many years later we added a closed contact and fed the coil through it. This made a buzzer which was easier (for me) to copy.
This was a marvel being able to travel and listen to the radio. It was also a battery killer. You did not forget and leave it on with out the motor running to many times (don't ask how I know this)
So everything is "NEW" and nothing is. The difference today is the transistor being used instead of the vibrator. This 'boost' supply takes 3 volts input and produces 9 volts output.
The one thing they all have in common is the inertia of a magnetic field in a coil of wire. When you apply power the coil opposes the expansion of the field and absorbs energy. When the power is removed the coil opposes a decreases in current and uses the stored energy to maintain current as long as possible. If you apply 0.5 volts through a low resistance copper wire and let the field build to its max current and then remove the source the coil will attempt to maintain the current through any path it can find. So if your source can produce 1ma through the "short" circuit represented by the transistor (switch) and the coil it will maintain that 1ma through the LED as it discharges. There is no free energy but the high voltage pulse is a short duration. The eye blends the pulses of light and it is good.
The ladies did a great job and hopefully learned things from this project that can be applied to future projects.
My latest project was a circuit to power a 12 volt LED from a USB supply. I have a solar charger for the USB supply and a boost supply much like the one above. It works but now I hang my head in shame that I bought the supply when I could have followed the ladies example.
Maybe another project in the making?