SequenceGenerator

SequenceGenerator is a software component or utility that produces a sequence of values according to a defined rule. It can be deterministic, following a fixed formula, or non-deterministic, incorporating randomness. It is commonly used in programming, mathematics, and data generation tasks.

Implementation typically exposes an interface to obtain the next value, such as next(), generate(), or an iterator/generator. They may support starting parameters, explicit length or termination conditions, reset capabilities, and options to access the current value or remaining terms.

Common sequence types include arithmetic progressions (constant difference), geometric progressions (constant ratio), Fibonacci-like sequences (recurrence relations), and user-defined recurrences. Sequences can also be non-numeric or pseudo-random, used for testing or simulation, with deterministic seeds when reproducibility is required.

In software, SequenceGenerator is often realized as an iterator or generator object that yields values on demand, enabling lazy evaluation and low memory usage. Languages provide different APIs: Python generators, Java streams or iterators, and C# enumerable sequences. Implementations may employ memoization to cache results or support infinite sequences with explicit bounds.

Applications include numerical experiments, algorithmic problem solving, testing, simulations, and procedural content generation. Design considerations cover determinism and reproducibility, performance and memory usage, thread safety, overflow handling, and clear termination behavior. Related concepts include iterators, generators, recurrence relations, and random number generators.

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