Three individual flashing circuits that use an LM3909 LED flasher/oscillator IC create the appearance of a pseudo-random firing order. The combination of CX!RV C.JRb, and C^R control the blink rate, which is between 0.3 and 0.8 s, and the inherent wide tolerance range [-20% to +80%) of standard electrolytic capacitors add to the irregularities of the blink cycles. The continuous current drain is about 10 mA; however, if you decrease the values of R4 through R6 or CI through C3 in order to increase the blink rate, the current will then increase proportionally.
Note in particular that external current-limiting resistors aren`t needed for LED 13 through LED18; the resistors are built into the ICs. LED10, which serves as the tree`s star, is a special kind of flashing LED that blinks continuously at a fixed rate.