The circuit above slowly fades an LED on and off. This effect is also known as the breathing LED or the Apple LED. The circuit is built entirely around transistors, no IC's or microcontrollers were used.
The circuits consists of 2 distinctive parts. T1 and T2 form together with C1, C2, R2, R3, R5 and R6 a classic astable multivibrator circuit. T3, C3, R1, R4 and R7 form a LED fader circuit. When the left side of R4 is connected to the supply voltage, capacitor C3 is charged and the base current of T3 increases which in turn fades the LED slowly on. When the left side of R4 is left unconnected, C3 discharges slowly via R7, fading the LED off again. Diode D1 is added to avoid C3 to discharge too quickly when T2 is conducting.
The astable multivibrator circuit output frequency is choosen to match the fade on/off time of the LED fader circuit.
As an alternative you could add a second LED fader circuit and connect it to the collector of T1. Then you will get 2 alternating breathing LEDs.
The circuit runs well with a supply voltage of 5V, but higher voltages are possible. Depending on the LED you use and the supply voltage, it might be necessary to experiment with the values R4, R7 and C3. We tested the above circuit successfully with a green and a white LED. When using blue LEDs on 5V, you can lower R4 to 100K otherwise the LED may be too dim. As R4 limits the base current of T3 it sets also the maximum brightness of the LED. For a faster/slower breathing LED, you can also experiment with the astable multivibrator circuit.
Nowadays you can get 10 microfarad (and even higher) ceramic multilayer capacitors in 1206 SMD packages. When using SMD parts, the entire circuit can be built very compact. Electrolytic capacitors can be used too of course but you will have to pay attention to polarity.
Please note that the circuit on initial start up (after applying power) due to the fact that C3 is completely discharged may need a few seconds before the LED starts fading on and off.
Below you will find some eagle files, gerber files and a PCB layout in PDF. Note that the PCB layout is not tested.