In the circuit below, a twin-T sine oscillator, build around Q1, is used to slowly fade in/out a LED.
The twin-T filter is formed by R3,R4,C1 (first T) and C2,C3,R6 (second T). The T-filters give a 180 degrees phase shift at the resonance frequency, at which the impedance of the filter is at its minimum.
The divider created by R1 and R2 is used to offset the voltage that is converted into a current by Q2 and R7. R1 and R2 are tweaked to get a sinusoidal voltage over R7 that is going to 0V, so the LED goes completely off.
R7 is chosen, so the current through the LED is approximately 10mA.
R6 is added to limit the current, so the LED can not be damaged while experimenting.
The oscillator has a period of about 3 seconds.
Use a high efficiency LED for LED1 for the best effect, because their brightness is pretty high at 10mA.
Click here to download the LTSpice simulation of the Twin-T sinusoidal LED fader
The oscilloscope picture below shows the voltage over R7 (=100E), that represents the current through the LED :