Coupled Janus Oscillator Network

This image presents a vivid phase portrait of a network of coupled Janus oscillators. Systems of coupled oscillators are powerful models for understanding emergent behavior in complex domains ranging from synchronized firefly flashes and neural rhythms to power grid stability and market dynamics. Rendered here with aesthetic intent, the image reveals the intricate choreography that such systems can exhibit.

Each pixel represents a Janus oscillator: a minimal composite unit formed from two internally coupled phase oscillators, which are further coupled to their neighbors in a lattice. Regions of similar hue denote local phase coherence. These are zones where oscillators are phase-locked through mutual coupling interactions, forming patches of synchrony that drift, collide, or dissolve.

Though the image lies on a 2D plane, the underlying topology is that of a torus—the edges wrap around, eliminating boundaries and allowing waves of phase interaction to propagate unimpeded, as if on the surface of an endless drum.

This was written as a GLSL fragment shader and feedback is used to animate the system. A bump map is calculated to creating false lighting to give depth and specular highlights.