Equilibrium tide. The Moon (and Sun) pull harder on the near side of Earth than on the far side, so the ocean is stretched into two bulges. A body of mass M at distance d raises an equilibrium tide of height ~ (3/4) (M/M_E) (R/d)^3 R, proportional to M/d^3. The Moon wins over the Sun by about 2.2 : 1, so S2 is roughly 0.46 of M2.
Two bulges, two tides a day. A point on Earth passes under both bulges once per lunar day, giving the semi-diurnal term A cos(2 (H - H0)). With the Sun at hour angle H_s = 2 pi t / 24 h and the Moon at H_m = H_s - D (D is the Sun-Moon elongation, 2 pi t / 29.53 d) this model uses eta = A_M cos(w_M2 (t - lag)) + A_S cos(w_S2 (t - lag)) with w_S2 = 2 pi / 12 h and w_M2 = 2 (w_sun - w_syn) = 2 pi / 12.4206 h.
Beating gives spring and neap tides. Two close frequencies add up to a slowly varying envelope E = sqrt(A_M^2 + A_S^2 + 2 A_M A_S cos((w_S2 - w_M2) t)). Its period is 2 pi / (w_S2 - w_M2) = 14.765 d, half a synodic month: range 2(A_M + A_S) at new and full Moon (spring), 2(A_M - A_S) at the quarters (neap). The Experiments panel measures this period from a simulated signal and compares it with the formula and with the published M2 period.
Island effects. The flats are a fixed profile, so the shoreline is where the profile height equals sea level. The central basin fills through 12 channels once the sea tops the channel sill (-0.35 m) and drains only down to that sill, then seeps; each of the 12 tide pools holds water below its own spill rim and seeps slowly (0.04 m/h). The boat grounds when sea level is below bed (-1.6 m) plus draft (0.9 m).
Honest simplifications. Real tides are not equilibrium tides: ocean basins resonate, Earth rotates under a moving wave, the Coriolis force and coastlines shape amplitude and timing, so real ranges vary from centimetres to over 10 m and highs arrive hours after the Moon passes. The "port lag" and amplitudes here are free parameters, not a particular harbour. Only M2 and S2 are modelled (no N2, K1, O1, Moon declination, perigee or shallow-water terms); the lunar declination is zero and the season slider only affects the Sun's height. The island is not to scale: vertical relief is strongly exaggerated, the sea level range is shown in metres on a 13-unit disc, and the day/night sky is simplified. Storm surge is shown as a plain offset in metres.