In 1202 Fibonacci investigated how fast rabbits could breed.[more]
Suppose a pair of rabbits, one male and one female, start a family. Rabbits mature at the age of one month (labeled "m") and a female produces a new pair of rabbits (labeled "n") at the end of its second month.
Suppose that the rabbits survive forever and that a female always produces one new pair (one male, one female) every month, giving the original pair and a new one.
How many pairs will there be in eight generations?[less]
The sequence can be reproduced by a substitution system, replacing every "m" in one month by "mn" in the next and similarly replacing every "n" by "m".