The Golden Ratio of Falling Stars by Jeffrey Ventrella
Every time the dot traces out a new pentagram, it rotates by 36 degrees, and it lessens the length of its stroke by a value of 0.61803399...(the inverse of the golden ratio, which is 1.61803399...).

The golden ratio is determined by calcualting a Fibonacci series, and then taking the ratio of the two last values.

See more geometrical explorations at Ventrella.com