Slow On Off (brightening/dimming) LED with Caps?

I'm not sure about this but wondered if the attached simple circuit would work. You can slowly dim an LED with a cap in parallel to it (and its resistor) when you turn it off but the trick is to slowly turn the LED back on (slowly brightens). I thought some arrangement of cap, resistor and/or inductor would do the trick. I don't have a high value cap to experiment with.

Of course with caps, the charging and discharging curve is not linear.
I'm just trying to make this simple without having to use a PWM circuit but maybe I have to.

Any suggestions???

Led circuits page - Little more than half way down on the page

The_Ad_Lab: Multiple LED pulsing via a 555 timer

Fading LEDs - RED - Page58

Any of those should work for you depending on what parts you have laying around.