The circuit shown here is formed of nine inverting transistor amplifier stages connected in series with an LED connected between emitter and ground. The output of the final stage connected to the input of the first stage. The principle is similar to the ring oscillator described by the author elsewhere in this edition. Similar but not identical, since the stages in this circuit have additional delay elements formed of a 33 kΩ resistor and a 47 µF electrolytic. The circuit operates with an odd number of LED stages of your choice, for instance with nine (as shown here).
The project oscillates very reliably and the way the twinkling LEDs fade in and out is quite a novelty. If you watch just two LEDs, they look like a simple blinker as there is always one lit LED next to a dark one. But with the lights circulating it looks a lot more complicated. Any disturbance will also travel around the ring. To watch the effect take a look at this YouTube Video: