A recurrence relation defines each term of a sequence using previous terms.
They model feedback, growth, and dependency across mathematics and computation.
Example (Fibonacci):
F(n) = F(n−1) + F(n−2)
Applications: algorithms, dynamic programming,
combinatorics, population models.
Fibonacci Generator
🔍 Beyond Fibonacci: Deeper Recurrence Structure
Not all recurrence relations behave like Fibonacci. More general recurrences
reveal deeper algebraic and number-theoretic structure.
Linear recurrences: solved via characteristic polynomials and eigenvalues
Nonlinear recurrences: can exhibit chaos, bifurcation, or modular cycles
Closed forms: arise through diagonalization or generating functions
Modular recurrences: produce Pisano periods and residue dynamics
These ideas connect recurrences to algebra, dynamical systems, and even
cryptographic constructions.
