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The science
A taut thread of tension T and linear density mu = rho pi d^2 / 4 carries transverse waves at v_t = sqrt(T/mu), and compression waves at v_l = sqrt(E/rho) (about 2.3 km/s for silk with E = 6 GPa). The web is a graph of radial threads and capture rings; arrival times come from a shortest-path (Dijkstra) search with edge length / speed.
The spider, resting at the hub, compares the amplitudes arriving on its legs: the vector sum of the leg amplitudes points to the prey. The delay between the fast longitudinal and slow transverse waves gives the distance, d = Dt / (1/v_t - 1/v_l), like the S-P delay used for earthquakes.
Simplifications: capture spirals are drawn as closed rings, amplitude decays as A0 exp(-beta d) 0.93^n (damping and junction losses) instead of full wave scattering, no thread sag and no aerodynamic damping. Silk constants are typical orders of magnitude, not a specific species. The animation is slowed down by a factor of about 10,000.
What to try
- Press Tight web versus Slack web: the wave speed and S-P delay change with the square root of the tension.
- Click different places and compare the estimated direction with the red dashed line.
- Use Big web, small prey and see the signal fall below the spider threshold.