Same firebrand physics as the flight-path version, viewed two different ways at once. Each ember still falls at a size-dependent terminal velocity while relaxing toward the wind speed horizontally, and its diameter still shrinks at a steady burn rate:
v_t(d) = k·√d (terminal fall speed)
τ = v_t / g (relaxation time to gravity/wind)
dv_y/dt = (−v_t − v_y)/τ, dv_x/dt = (U_wind − v_x)/τ
d(t) = d0 − β·t (diameter shrinks as it burns)
Left map — a parameter-space sweep: every pixel is its own full flight simulation for that (wind, diameter) pair, colored by how far a hot-landing ember travels before it either burns out mid-flight (dark) or lands cold (dim). The bright ridge is the "sweet spot" the theory predicts — mid-sized embers survive long enough to fall and ride the wind farther than either extreme.
Right plot — a live phase portrait: instead of plotting embers moving through physical space, it tracks each one's downwind distance against its remaining diameter as both evolve together in time. The curve bends because fall speed and burn rate both depend on the shrinking diameter — a relationship invisible in a spatial flight-path view.
- Wind speed / diameter sliders — move the crosshair on the left map and change the burst parameters on the right.
- Plume lofting height — more hang time before landing; the map recomputes to match.
- Launch ember burst — releases a fresh sampled batch (±30% size spread, matching the 3D version) into the phase plot.
Note: the burn rate is sped up for interactivity — real firebrands typically smolder for tens of seconds to minutes.