Cosmic Ray Air Shower Ground Footprint

A single ultra-high-energy cosmic ray striking the upper atmosphere sets off a cascade of billions of secondary particles that spreads into a broad footprint by the time it reaches the ground — this is the pattern a real surface detector array actually measures. This simulator renders that footprint in 3D: secondary particles rain down and land following the genuine Nishimura–Kamata–Greisen (NKG) lateral distribution function, while a grid of ground stations lights up to show the local density each would record. Tune the primary energy, the shower's age past maximum, and the observatory's altitude (which sets the Molière radius), and read off the total shower size and the S(1000) ground density — the exact quantity observatories like the Pierre Auger Observatory use to estimate a cosmic ray's energy without ever counting every particle.