This 2D companion runs the identical Kuramoto phase-oscillator equations as the 3D version through plain Canvas 2D drawing: N phase oscillators sit on a flat ring, colored by their natural frequency, each pulled toward the population's mean phase with strength K. Every control carries over one-to-one — oscillator count N, coupling K, frequency spread σ and playback speed, plus the Perturb and K=0/K=3 preset buttons — while a live order-parameter trace and a phase histogram give a always-readable readout of the incoherent-to-synchronized transition.