Generator Iterator

Purpose-built to generate deterministic sequences from a seed using a user-defined recurrence. It targets developers, researchers, and data scientists who model discrete-time processes, test convergence, or benchmark recurrence-based algorithms. The engine evaluates a recurrence with variables i (step index) and s (current state) to produce s_{n+1} from s_n. It supports linear, nonlinear, and user-defined expressions, with optional constraints like modulus m and cycle detection. The tool emphasizes safety by sandboxing expression evaluation and rejecting arbitrary code execution while providing full reproducibility across runs. Users can inspect the entire sequence, the final value, and basic statistics such as min, max, and mean. Outputs are deterministic given the same inputs and can be exported for further analysis. This tool is beneficial for algorithm researchers validating recurrence behavior, software engineers prototyping stateful models, and data scientists exploring sequence properties under constraints. Its unique value lies in combining safe evaluation, optional constraint features, and straightforward export to common data formats, without requiring programming beyond the recurrence expression. Core features include: seed input, recurrence expression with i and s, iteration count, optional modulus, cycle detection, sequence output, and metadata. Use cases include testing convergence of recurrences, simulating discrete dynamical systems, and benchmarking iterative algorithms in a reproducible manner.