D2 forces C7 to discharge quickly when power is removed. To set how fast it thinks, we need an external crystal X1 and associated capacitors C1 and C2. Note that the crystal could be replaced by a 12MHz ceramic resonator. This allows the '2051 to execute an instruction every 1 or 2us. As you can see from the schematic, the 30 LEDs are connected in an X-Y matrix.
Engineering is full of trade-offs or compromises.
I wanted a 5 pointed star so the number had to be divisible by 5. For aesthetic reasons, we need an even number of LEDs per point. This process is repeated for each column in turn taking 10ms for a full cycle. The minimum practical multiplexing frequency is about 100Hz which is the frequency used by the star. The power supply uses the ubiquitous 7805 three terminal regulator with bypass capacitors C4 and C5.