2D companion to the 3D scene: the same positional mechanosynthesis chemistry — the original "molecular assembler" concept (Drexler, Freitas, Merkle) — drawn as a flat pick-and-place diagram instead of rendered spheres. A rigid tip picks up one feedstock unit at a time and places it directly at a chosen lattice site, forming a bond only if the placement error falls inside a narrow Gaussian acceptance window.
δ = placement error (pm), sampled ~ N(0, σ_total)
σ_total² = σ_tip² + σ_thermal²
σ_tip = 60·(1 − rigidity) [mechanical compliance of the tip]
σ_thermal ∝ (T − 100 K) [Brownian jitter of the feedstock atom]
P(bond) = exp( −δ² / (2·σ_accept²) ), σ_accept ≈ 35 pm
- Tip rigidity — a stiffer cantilever injects less positional noise per attempt (σ_tip shrinks), directly raising the average bond-acceptance probability.
- Feedstock temperature — hotter feedstock atoms vibrate more before capture, adding an independent noise term in quadrature (error propagation), which lowers yield even with a perfect tip.
- Assembly speed — how often the tip attempts a pick-and-place cycle; it changes throughput, not the per-attempt success probability.
- A failed attempt drops the atom back into the feedstock pool and the tip retries the same open site — exactly the retry-until-bonded strategy proposed for real mechanosynthesis tool-tips (e.g. DCB6Ge dimer placement on diamond C(110)).
Two target lattices are offered: a 2D triangular close-packed lattice (the flat analog of the stiff tetrahedral diamond framework the real proposals target) and a square lattice (an easier four-neighbor geometry, useful for seeing how yield changes when there is more angular tolerance per bond).