The 3D version of this simulation buds each polyp along an explicit free-space vector blended from the parent's own axis, a light vector, a current vector and a crowding-repulsion push. This 2D version reproduces the same growth phenomenology through a different, grid-native mechanism cited by the same coral-growth literature (Kaandorp's accretive models): a scalar light-availability field φ is solved on a 2D lattice every frame by relaxing Laplace's equation, φ=1 at the water-column top, φ=0 wherever tissue already exists (the colony absorbs light/nutrient before it diffuses further), and no-flux walls elsewhere:
∇²φ = 0 (relaxed by Gauss–Seidel sweeps each frame)
φ = 1 at top boundary, φ = 0 on occupied (colony) cells
P(cell accretes) ∝ φ(cell)^η · (1 + 0.3·cosθ_current) · (1 − local density)
This is the Laplacian-growth / dielectric-breakdown formulation of diffusion-limited accretion: the harmonic field's gradient at the colony boundary is the growth-probability measure, so a higher sharpness exponent η produces the same thin, tip-splitting branch fractals that high phototropism produces in the 3D vector model, while low η spreads probability evenly across the boundary and produces a dense, rounded, encrusting mass — without ever explicitly computing a 3D budding vector.
- Budding rate — expected new accretion events per second, scaled by current polyp count (same Poisson-per-polyp rule as the 3D model).
- Phototropism — maps to the field-sharpness exponent η = 1 + 3·k. Low η (~1, classic DLA) → rounded, massive growth; high η (~4) → thin, upward branch fractals that race for the φ=1 boundary.
- Crowding avoidance radius — local occupied-cell density within this radius multiplicatively suppresses accretion probability, exactly mirroring the 3D model's "too crowded, stalls" rule.
- Current direction — biases accretion probability toward candidates that lie in the current's direction relative to their parent cell, at the same 0.3 relative weight used in the 3D model.
*Scale is illustrative (arbitrary sim units), not a literal centimetre measurement.