Where does this show up in the real world?
Although it looks like a fun math toy, the underlying ideas crop up everywhere:
| Domain | Example & why it’s similar |
|---|---|
| Warehouse & logistics | Pallet or coil stacking and bin-packing software deciding where to place incoming items so that weight limits, stability and retrieval order are satisfied. |
| Statistics & experimental design | Random assignment of test subjects or plots to treatments must ensure no collision/duplication. Weighted randomisation is common in clinical trials (e.g. block randomisation). |
| Physics | Monte-Carlo simulations of lattice gases or spin models (Ising, percolation). Occupying lattice sites at random without duplicates is step 1 before applying interaction rules. |
| Chemistry & materials | Random sequential adsorption models how molecules stick to a surface until no further placement fits |
| Biology | Simulating colonisation of cells on a Petri dish or receptors on a membrane uses the same collision-free random placement. |
| Computer graphics / games | Procedurally scattering trees, loot or NPCs on a map while avoiding overlap; or tetrimino/brick-fall games with gravity constraints. |
| Neuroscience | Generating synthetic but biologically plausible neural micro-connectomes often starts by placing neuron somas randomly in 3-D space subject to minimal spacing constraints. |
| Network design | Random node placement in wireless-sensor-network studies, where you must avoid duplicate coordinates and sometimes enforce “no floating node unless it can connect to two below” analogues. |
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