capacitor - How to gradually light up an LED

With a circuit of a charged capacitor, a resistor, and an LED, I can create a lighten up LED that gradually dims until the capacitor run out of charge.

With a combination of a battery, capacitors, resistors, and LED, is it possible to create the opposite effect, that is an LED that gradually lighten up? If not, what kind of components that I might need to produce this effect?

Answer

The other component you need is a transistor. Try something like this, and it should take several seconds to turn on.

^{simulate this circuit – Schematic created using CircuitLab}