Feed a river with sediment, watch the delta grow and the channel jump. A simplified teaching model (a cellular, parcel-routing model on a 16 km square), not a forecast for any real delta.
The science
Sediment budget (Exner equation). The bed elevation η obeys (1 − λ) ∂η/∂t = −∇·qs. The model moves sediment as parcels (each carrying a volume q) that walk downhill; where the parcel carries more than the local capacity it deposits, where less it erodes. Every cubic metre deposited or eroded changes η of one cell, so the budget is closed exactly: fed = Δbed volume + suspended + lost to deep sea. Supply uses a dry bulk density of 1300 kg/m³ (porosity λ is folded into that).
Capacity and avulsion. Capacity grows with the bed slope along the path, qcap = q0 (S / S0) (S0 = 1.2·10⁻³). Where slope falls, sediment drops, the channel bed rises, and once the channel is higher than its surroundings water steps over the bank and takes a lower route: an avulsion. The counter flags the dominant mouth moving more than nine cells (about 0.9 km) and staying there.
Mouth bars and plume. In the sea the capacity collapses and deposition is fastest in shallow water, which builds mouth bars that split the flow. A quarter of the sea deposit goes into a suspended-mud field that diffuses and settles slowly (the tan swirls).
Waves and sea level. Wave reworking is a diffusion of the shoreface bed, ∂η/∂t = ν ∇²η, kept below the explicit stability limit ν Δt / Δx² ≤ 0.25. Relative sea-level rise raises the sea surface at the chosen rate (mm/yr); subsidence has the same effect and is not modelled separately.
Honest simplifications. No hydrodynamics, tides, vegetation feedback, river meandering or real grain-size sorting; the parcel rules are teaching rules, so channel patterns and avulsion timing are qualitative. Valley, ridge and tree meshes are made in Blender; the delta surface is computed live and drawn with Three.js. Vertical exaggeration 4×.