Shown left is the main part of the circuit. An astable formed by IC1a/b drives a 4-bit binary counter IC2, which is decoded by the 3-8 line decoder IC3, to provide the required sequenced outputs.
To make the sequence reverse, the up/down input to the counter is controlled by a bistable formed from IC1c/d. This sets the U/D input high when output 0 is high so that the counter counts up, then is toggled low by output 9 to reverse the direction of count. This is then repeated indefinitely giving an output chase backwards and forwards.
The speed of the chase can be adjusted by VR1 which alters the speed of the astable.
This section is repeated 10 times for each output (Out0-9), to increase current drive to the LEDs or bulbs. If using bulbs then change R12-21 with a link wire. The 2N3904 has a maximum current of 200mA. This can be replaced with a higher device such as TIP122 darlington giving over 1 amp capability. There will be a slight drop in output voltage due to the voltage drop of the extra transistor. The pin connections are the same.
The capacitor C2-11 gives the output a slow switch off time resulting in a blurred chase.
Finally D1 prevents damage through reverse power connection with C3 and C4 decoupling the supply.