The Cycle

The Cycle visualization drives the EOC system through an automatically cycling rho (ρ) parameter — rising from subcritical through the bifurcation threshold and into the chaotic regime, then falling back. Three synchronized panels display the attractor in real time.

The key moments to observe: as rho rises through ~24.74, the single-wing trajectory begins making excursions toward the other wing. Wing transitions become more frequent. In the high-rho phase, the trajectory visits both wings unpredictably. As rho falls back below the threshold, the system settles again — but not necessarily into the same wing it started in. This asymmetry is structural.

• ρ (rho) cycling range: Typically 15 to 35, sweeping through subcritical, transitional, and chaotic regimes.
• σ (sigma) = 10: Standard engagement tracking rate.
• β (beta) = 8/3: Standard consolidation decay rate.

The full parameter controls are available on The Controls page.

This page runs a live Three.js visualization in your browser. The mathematical computation uses fourth-order Runge-Kutta (RK4) integration with step size dt = 0.005. Desktop browsers use Web Workers for computation; mobile uses a main-thread fallback.

The equations and formal framework are on The Science page. The intuition for what you are watching is on Understand.