Each bead carries a fixed ratio of C quantum-dot emission colors (spectral channels), each dosed at one of L discrete intensity levels. This diagram plots that C-dimensional intensity vector directly as a 2D point — not a spatial picture of beads in a dish, but the actual ratio/code space the decoder works in — by summing each channel's fraction along its own compass/ternary axis:
code capacity N = L^C − 1 (excludes the all-off blank code)
channel level v_k ∈ {0,…,L−1}, k = 1…C
measured m_k = v_k/(L−1) + noise, noise ~ N(0, σ²)
decoded code argmin over all codes of Σ_k (m_k − code_k)²
plot position Σ_k frac_k · axis_k (axis_k = unit vector for channel k)
Because the per-channel axes are arranged symmetrically (2 orthogonal for C=2, 120° apart for C=3, compass points for C=4), a bead whose channels are all equal partially cancels toward the centre — exactly like a chromaticity diagram, where equal color mixture reads as "white" near the origin. Pure single-channel codes push hardest toward their own axis tip. The nearest-code decoder itself always runs in the full C-dimensional fraction space (never in this 2D projection), so decode accuracy numbers are exact even though two different high-dimensional codes can occasionally land near the same 2D spot for C=4.
- Faint dots — every valid code in the current space, plotted at its true ratio position, tinted by its own combinatorial color.
- Solid dot — a bead's true (ground-truth) barcode position.
- Ring + tether line — the detector's noisy reading, pulled off the true position by Gaussian scatter; green ring = decoded correctly, red ring = the noise pushed it into a neighbouring code's territory.
- Channels / Levels — set L and C; capacity N = LC − 1 grows fast, packing codes closer together in ratio space.
- Detector noise — Gaussian scatter added to every channel reading before decoding, modelling photon shot noise and spectral crosstalk between adjacent QD emission peaks (Han, Gao & Nie, Nature Biotechnology 2001).