Random

Randomness is the absence of a predictable pattern in the outcomes of a process. In probability theory, a random process yields outcomes that cannot be determined with certainty but can be described statistically by a probability distribution. It does not imply chaos; rather, repetitions follow a probabilistic model. Common examples include coin tosses, dice rolls, and fluctuations in complex systems.

Randomness can be generated by physical processes (true randomness) or by computational algorithms (pseudo-randomness). True randomness derives entropy from nondeterministic phenomena, such as radioactive decay or thermal noise. Pseudo-random number generators produce sequences that appear random but are determined by a seed; they are usually sufficient for simulations but require caution in cryptography where unpredictability is essential. Randomness is described by distributions: a uniform sequence has equal probability for each value, and independence means successive values do not influence each other.

Assessing randomness uses statistical tests for uniformity, independence, and absence of detectable patterns. Standards such as NIST SP 800-22 are used to evaluate generators. Entropy, a measure of uncertainty, quantifies a source's randomness.

Applications include Monte Carlo simulations, randomized algorithms, sampling, and cryptography. In physics and philosophy, randomness relates to determinism and quantum phenomena, where some interpretations posit intrinsic randomness, while others suggest underlying determinism hidden by complexity.