Intrínseques

Intrínseques is a term used in theoretical discussions to denote a class of sequence-like objects whose evolution is governed entirely by intrinsic state and internal transition rules, with no dependence on external inputs after initialization. The name combines intrinsic with sequence and is used to emphasize self-contained generation within a dynamical or computational framework.

In formal terms, an intrínseque consists of a state space S, an initial state s0 in S, a transition function T: S → S, and an emission function E: S → V, where V is a value set (often the integers). The generated sequence (a_n) is defined by a_n = E(s_n) with s_{n+1} = T(s_n). Some variants allow stochastic transitions, but the core idea is that all structure arises from internal rules and state, not from external time-varying inputs. A common specialization is finite-state intrínseques, where S is finite, yielding periodic or eventually periodic sequences. More expressive forms may use richer state spaces or non-deterministic transitions.

Examples are typically simple and illustrate the principle of internal generation. A two-state intrínseque with states s0 and s1, where T(s0)=s1, T(s1)=s0 and E(s0)=0, E(s1)=1, produces the regular sequence 0, 1, 0, 1, …. Other examples explore richer internal architectures while preserving the autonomous, internal nature of the rule set.

Relation to related concepts includes automata theory, cellular automata, and dynamical systems. Some scholars view intrínseques as a unifying lens for self-contained generation, while others critique the notion as overlapping with established frameworks. See also automata, dynamical systems, and discrete sequences.