Every asteroid is a real Kepler orbit: semi-major axis a (AU) fixes its mean motion via Kepler's third law, n = 2π / a^1.5 rad/yr, so an asteroid at a = 2.5 AU orbits in 2.51.5 ≈ 3.95 years — the same relation that gives Jupiter its real 11.86-year period at a = 5.2 AU. Position is approximated as r ≈ a·(1 + e·cos M), θ = M (mean anomaly standing in for true anomaly — accurate enough to show the belt's structure, not a precision ephemeris).
Three narrow bands sit at exact Jupiter mean-motion resonances: 3:1 (2.50 AU), 5:2 (2.82 AU) and 2:1 (3.27 AU) — an asteroid completing exactly 3, 5:2 or 2 orbits for every one of Jupiter's gets the same gravitational tug at the same point in its orbit, cycle after cycle. That coherent, repeated kick pumps up eccentricity until the orbit becomes chaotic and the asteroid is ejected from the resonance — discovered by Daniel Kirkwood in 1866 and confirmed by every asteroid catalogue since. Asteroids inside a resonance band are ejected with probability ∝ (Jupiter mass)², matching the linear-in-mass forcing term squared for a stochastic kick rate; ejected asteroids are recolored and their eccentricity ramps toward a higher, unstable value.
The density histogram bins the live semi-major-axis distribution — watch the three Kirkwood gaps carve themselves out of an initially smooth belt as simulated time advances. This is why no planet formed between Mars and Jupiter: Jupiter's gravity stirred relative velocities too high for accretion, and the same resonances still clear out any wanderer today.