Yet another LED fader, but this time with a sinusoidal fading curve, generated by a Twin-T oscillator. The disadvantage is that you can not change the frequency of the sine wave with a potmeter, but the circuit is simple, yet effective. To change to another frequency, the 2 T-filters have to be adjusted individually. The circuit is designed for a power supply of +12V. The sine oscillator needs a certain gain to maintain the oscillation, and thus the power supply can not varied widely,

The 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 2 T-filters give a 180 degrees phase shift at the resonance frequency, at which the impedance of the filter is at it's 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 dimensioned to get a sinusoidal voltage over R7 that is goes to 0V, so the LED goes completely off.
R7 is choosen 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 3seconds.
Use a high efficiency LED for LED1 for the best effect, because their brightness is pretty high at 10mA.