Gene Regulatory Network Oscillator

A single gene can oscillate all by itself if its own output eventually shuts its own transcription down — with enough delay and enough cooperativity in the repression. This simulator renders the classic Goodwin model: mRNA X, protein Y and a repressor Z chained in a negative-feedback loop, each represented as a pulsing node whose glow tracks its live concentration, plus a phase-space trail that traces the trajectory of (X, Y, Z) through 3D concentration space. Tune the Hill cooperativity exponent past Griffith's stability threshold and watch the system cross the bifurcation from a damped spiral into steady state to a genuine self-sustaining limit cycle — the same mathematical structure that drives real circadian and synthetic genetic clocks.