The Fibonacci sequence tends to grow at the Golden ratio (approx 1.618) while the actual conversion is ~1.609 so it does usually work well.

In fact any Fibonacci-like sequence with different starting numbers eventually will work, after it gets past the initial crop of bad conversations, as such sequences have growth rates than tend toward the golden ratio as they grow long enough.

For example starting from 2, 9 instead of 1, 1:

2, 9, 11, 20, 31, 51, 82

20 mi ~= 32 km 31 mi ~= 50 km 51 mi ~= 82 km