generating

Generating is the act of bringing something into existence or causing a particular result to come about. The term is used across disciplines to describe the production or formation of data, materials, ideas, or structures, often from a defined set of inputs, rules, or processes.

In mathematics, a subset S of a structure X generates X if X is the smallest substructure that contains S and is closed under the relevant operations. The substructure obtained from S is called the substructure generated by S, and S is called a generating set. Examples include groups generated by a set of elements, vector spaces generated by a set of vectors through linear combinations, and rings generated by a set under addition and multiplication.

In computing and information science, generation may refer to producing sequences, files, or content. Random number generation uses algorithms to produce sequences that exhibit statistical randomness, often with a starting state called a seed. Generative AI refers to models that learn a data distribution and can produce new examples, such as text, images, or code, from prompts or conditions. Related concerns include quality, controllability, and bias.

In science and engineering, generation also denotes the production of energy or signals. Energy generation converts fuel or other resources into usable power, while signal or waveform generation creates timing or carrier signals in communications and instrumentation.