blinking LED with one capacitor oscillator circuit

I don't like the idea to use a component in a different way than the standard for the component. Using the internal resistance of the transistor is not like using the base of the transistor : D

Sure you can still get unijunctions:-
unijunction choice of 17

Now what was even rarer was the programmable unijunction or PUT. You could set the breakdown voltage by the ratio of two resistors.
I used to use a lot of these in the 60s.
You can still get these too, although not in one off quantities. programmabel unijunction

op-amp?

BorislavLukanov:
op-amp?

Yes use liner ramp.
http://www.edn.com/design/analog/4438481/Linear-ramp-generator-uses-one-op-amp
When the ramp is below the forward voltage it will be off and above it it will be on. Make sure your op amp can supply the current the LED needs.

I think we're talking about tunnel diodes.
They are (or were) widely used in microwave (Giga Hz) circuits.
Leo..

the simple relaxation oscillator with tunnel diode looks cool/fun : D

MarkT:
The old-school answer to this question is "use a unijunction transistor relaxation oscillator". I've
never seen a unijunction transistor, even way back when, I doubt you'll find one these days!
Unijunction Transistor and UJT Relaxation Oscillator

Wawa:
I think we're talking about tunnel diodes.
They are (or were) widely used in microwave (Giga Hz) circuits.
Leo..

I built a tunnel diode FM transmitter back in the day.

Smajdalf:
Tested and it WORKS. I used unknown NPN BJT (fake LM35), circuit from link in post #9 and the LED is flashing nicely. 9V was not enough but adding one AAA to get 10.5V made it. There is about 9.8 V over the cap and around 8.2V CE voltage (measured by DMM, changing quickly; LED blink much slower when measuring the transistor).

From the first and third video it appears that the flash interval isn't very stable. I'm curious if this is just an oddity of the video or if you saw the same thing.

If it is unstable, it suggests that the reverse breakdown voltage is variable (localized heating of the junction perhaps?) which implies that 1) tuning the resistor values is absolutely necessary to get the circuit to work at all with any particular transistor (hence the OP's difficulty) and 2) it's not a particularly practical circuit.

As an aside, the circuit is similar to the ne-2 (neon bulb/negative resistance characteristics) flasher circuits I built back in the day, albeit those worked at somewhere above 90 volts. I managed to survive that phase, but once blew up an ammeter in spectacular fashion . . .

Grumpy_Mike:
Yes use liner ramp.
Linear ramp generator uses one op-amp - EDN
When the ramp is below the forward voltage it will be off and above it it will be on. Make sure your op amp can supply the current the LED needs.

looks interesting, I'll try and also some signal transformation from sine to triangular if possible or different types of signal generators