Expanding on that further --
Note that the LEDs won't turn all the way off at high supply voltage. The reason for this is that, the transistor drops ~0.6V, and the LED drops a minimum, whatever it does -- depends on color, 1.5-3.6V for red to blue types. Meanwhile, the capacitor voltage is controlled between 1/3 to 2/3 of the supply, by the 555. If the supply is 9V, the range is 3-6V. Subtracting 0.6V for the transistor leaves 2.4V as the minimum across the LED. A blue LED will be quite dim at that voltage, if not completely off; whereas a red LED will probably still be dimly lit. A 6 or 7V supply would be more appropriate in that case, or a resistor can be connected in parallel with the LED to make it see a lower voltage.
Note that the fade is approximately linear, which doesn't look right, visually. Ideally you'd have a gamma correction circuit, which causes the current to increase (towards full brightness) more rapidly, and decrease (towards cutoff) more gradually. Unfortunately, there isn't a simple way to implement this on the breadboard.
Tim