Siriekvationen

Siriekvationen is a fictional class of mathematical equations described in recreational mathematics and collaborative worldbuilding projects. The term combines a purported origin with the word equation, and it is used to describe a family of recursive relations that enforce a symmetric, self-referential constraint known as the sirie property. The concept is not part of established mathematical practice, but serves as a deliberate device for exploring ideas of symmetry and recursion in a controlled, imaginative setting.

Definition and form: In the fictional framework, Siriekvationen consists of a sequence S(n) defined for integers n ≥ 1 by a base case and a recursive rule that depends on several previous terms. A fixed function F governs how current terms are computed from a window of earlier terms, while a sirie constraint imposes that the multiset of certain past values remains invariant under a prescribed permutation of their indices. This combination creates a symmetry among the recent terms and can produce varying solution behavior depending on initial conditions and parameter choices.

History and usage: Siriekvationen was introduced in pretend mathematical literature and among puzzle communities in the early 2000s by a fictional figure named Sirie, and it has since circulated in collaborative wikis and game-like settings. It functions as a toy model to study self-reference, symmetry, and the dynamics of recursive systems. It is intended for educational and entertainment purposes and is not used as a formal object in real research.

Examples and properties: Simple variants may yield monotone growth, bounded oscillations, or more complex dynamics. Some parameter choices admit closed-form expressions, others lead to behavior reminiscent of chaotic systems. The framework highlights how constraint design shapes recurrence outcomes.

See also: recursive sequences, functional equations, self-reference, symmetry in mathematics.