This is the standard change-detection paradigm used in visual working-memory research (Luck & Vogel, 1997; Cowan, 2001), run here as a genuine 2D simulation rather than a flattened 3D scene. Each trial: a study array of N colored squares appears at scattered, non-overlapping positions, disappears for a blank retention delay, then a test array appears — on half of trials one item's color has changed. You judge "Same" or "Different".
The lower panel is not a picture of the array — it is an independently computed signal-detection ROC (phase) plane: the x-axis is your cumulative false-alarm rate F, the y-axis your cumulative hit rate H. Diagonal reference lines trace every integer capacity level:
K = N × (H − F) ⇔ H = F + K / N
diagonal for K=0 (pure guessing) through K=N (perfect retention)
Every completed trial re-computes (F, H) from the running tallies and plots a new point; the trail shows how your operating point drifts toward a particular K-diagonal as trials accumulate — the same formula the 3D version only reports as a number, made visible as trajectory in a 2D parameter space.
- K — estimated number of items truly retained. Typical adult visual working-memory capacity is K ≈ 3–4, regardless of how large the array is — the empirical basis for the popular "magic number 4".
- Set size N — above your true capacity, your ROC point should settle on the same K-diagonal even as N keeps rising: the extra items are guessed, not retained.
- Study time / delay — real experiments show capacity is largely insensitive to a longer glance or a longer delay once items are encoded; the ROC point should stay near the same diagonal across settings.
Real-world relevance: visual working-memory capacity predicts fluid intelligence scores, is reduced in ADHD and schizophrenia, and is the mechanism radiologists and air-traffic controllers push against when scanning multi-item displays.