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A Lagged Fibonacci generator is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator. These are based on a generalisation of the Fibonacci sequence.
The Fibonacci sequence may be described by the recurrence relation:
Hence, the new term is the sum of the last two terms in the sequence. This can be generalised to the sequence:
In which case, the new term is some combination of any two previous terms. m is usually a power of 2 , often 2 or 2. The ⋆ {\displaystyle \star } operator denotes a general binary operation. This may be either addition, subtraction, multiplication, or the bitwise exclusive-or operator. The theory of this type of generator is rather complex, and it may not be sufficient simply to choose random values for j and k. These generators also tend to be very sensitive to initialisation.