Presets
Playback
Habitat geometry
Camera
Layers
Quality
Model check
The science
Closure and carrying capacity
Each colonist consumes c units/yr; a fraction η is recovered (water loops, air regeneration, food waste). Net demand per person is c(1-η), so a resupply stream S sustains at most K = S / (c(1-η)) people. Raising η from 0.9 to 0.99 multiplies K by ten.
Logistic growth
dN/dt = rN(1 - N/K), exact solution N(t) = K / (1 + (K/N0 - 1)e-rt). The page integrates it live with fourth-order Runge-Kutta (fixed 0.05 yr step) and compares to the exact solution at every step.
Spin gravity
A hull of radius R spinning at ω gives floor acceleration g = ω2R, so ω = sqrt(g/R), rim speed v = ωR. Gravity falls linearly toward the axis: g(r) = ω2r. A head 1.8 m above the floor feels about 1.8/R less than the feet (3 % at R = 60 m, 0.06 % at R = 3 km).
Coriolis effect and comfort
In the rotating frame, moving bodies feel a = 2ω × v. Spin rates above roughly 2 rpm are widely cited as the point where many people feel motion sickness; larger radii allow 1 g at lower rpm, which is why real concepts are kilometres wide.
Independent numerical check
A ball dropped from rest (relative to the floor) at height h moves on a straight line in the inertial frame. It lands when |pos| = R, giving the exact time t = sqrt(h(2R-h)) / (ω(R-h)). This is compared to the naive sqrt(2h/g); the difference must equal the first-order Coriolis/geometry correction 3h/(4R).
Honest simplifications
One lumped resource instead of separate air, water, food, power and spares budgets; population growth is a fixed rate, not a human choice; hull structural stress, radiation shielding and thermal balance are not modelled. The animated spin is slowed by the factor shown, and the number of houses drawn grows as the square root of the fill fraction N/K (so a small colony is still visible), trees follow the recycling efficiency and greenhouses follow resupply: these are visual encodings, not census counts. Educational model only, not a design tool.