So, the R and C (the resistor and the capacitor) next to the 555 timer circuit gives its "timebase". This means the time (the speed) between the pulses it gives out. These pulses are then fed to the 4017 counter and it activates one output pin at a time depening on the incoming pulses. That basically it...
For fading you will need to use a microcontroller and a PWM signal to fade one or more leds in and out in a sequence.
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