The Fibonacci(n, a, b) generates the nth Fibonacci string, with initial values a and b. The arguments after the first are optional, and default to the strings  and , respectively.

Given starting symbols a and b, the nth Fibonacci string is defined by the recurrence Fibonacci( n, a, b ) = cat( Fibonacci( n - 1, a, b ), Fibonacci( n - 2, a, b ) ), for , and the initial conditions Fibonacci( 0, a, b ) = b and Fibonacci( 1, a, b ) = a. The length of Fibonacci( n ) is equal to the nth+1 Fibonacci number.

The Fibonacci procedure has option remember.