A Dynamical-Systems Formalization of the TRISIKON Principle in Expanded Cinema

TRISIKON (tiga situasi dan kondisi, three situations and conditions) is a directorial principle from Indonesian expanded cinema that composes three visual modes, documentation footage, animation, and live action, into one work and reads their collision as a dialectic between creative uncertainty and compositional order. Developed through practice-based studies, it has had no quantitative formalization. Here the three modes are placed on the cyclically symmetric axes of the Thomas flow, and the dialectic is identified with a single dissipation parameter that carries the flow between an ordered regime and a chaotic one. The structure is fixed by exact results proved here: the flow is dissipative, with a bounded absorbing set and a compact global attractor; it is equivariant under cyclic permutation of its axes; it has a saddle at the origin; and it contracts phase-space volume at a constant rate. Consequently its Lyapunov exponents sum to that contraction rate for every invariant measure, which also serves as an internal check of the computation. Each regime is characterized by the Lyapunov spectrum with its dimension and entropy rate, by a Gaussian and a nonparametric differential entropy, by the permutation entropy with its statistical complexity, and by an order parameter that provably vanishes when the symmetry holds. Four cases, an ordered baseline, a balanced breathing, a deconstructive regime, and a symmetry-broken mode-dominance regime, are separated consistently by every diagnostic. The formalization is a shared language between weak-chaos theory and the aesthetics of expanded cinema, not an empirical claim about film practice.