How this replication works
This page summarizes the original study and is explicit about every place this online version departs from it, so the replication can be judged fairly.
The stimuli
Each pattern is a row of 7 squares: 3 black, 4 white. There are exactly 7!/(3!4!) = 35 distinct arrangements, and all 35 appear here, exactly as in the original. The paper printed them on paper strips with a thin grey baseline "to orient the pattern and keep mirror-image patterns distinct" — the pattern strips on this site reproduce that same baseline.
Subsymmetries
A segment is any connected run of 2 or more squares within a pattern (regardless of color). Every 7-square pattern contains exactly 21 segments. A segment is a subsymmetry if it reads the same forwards and backwards. The paper's central claim: the number of subsymmetries in a pattern (out of 21 possible) predicts how cognitively simple it feels, far better than whole-pattern symmetry or the number of black/white blocks. In the original 35 patterns this ranged from 5 (least simple) to 9 (most simple) subsymmetries — this replication generates the same 35 patterns programmatically and gets the identical range, which is a good sign the definitions are implemented correctly.
The four experiments
| Original | Here |
|---|---|
| 1. Search — a participant is timed finding a target pattern within a random 5×7 array of all 35 patterns laid out on a table. | A target pattern is shown, and you click its match in an on-screen scrambled 5×7 grid. Reaction time is measured client-side (from the moment the target appears to the moment you click correctly) and sent to the server only once your run finishes, so network latency never pollutes the timing. The first few trials of each session are treated as warm-up and excluded from analysis, exactly as in the original ("the very sharp drop in search time which occurred during the first few patterns"). |
| 2. Subjective — a participant looks at all 35 patterns and points to them one at a time, simplest first. | All 35 pattern cards are shown; you click them in order from simplest to most complex. Your click order is recorded directly as a rank order. |
| 3. Memorization & confusion — a participant studies a "quartet" of 4 patterns for 30 seconds, then picks the same 4 out of a larger random array, most-confident first. Repeated over many quartets so each pattern is tested multiple times. | Same design: 30 seconds to study 4 patterns, then pick them from a scrambled set of 16 (the 4 originals + 12 distractors), most-confident first. You can do as many rounds as you like — because this is a "living" experiment collecting data from many participants over time, the paper's exact per-subject quota (each pattern tested exactly 4 times per subject) is relaxed in favor of pooling many people's shorter sessions, the same statistical logic the original paper used when it "obtained measures by summing over 14 Ss" rather than requiring subject-to-subject agreement on this task. |
| 4. Verbal description — two participants, unable to see each other, take turns: one describes a pattern in words, the other tries to place it correctly on their own array. | Split into two asynchronous steps so any two participants — anywhere, anytime — can pair up: first you describe a pattern shown to you in words; separately, you're shown someone else's written description and eight candidate patterns, and you try to pick the one they meant. |
Analysis
Each experiment produces one rank order of the 35 patterns (simplest = rank 1), with ties handled by averaging, exactly as Kendall's rank-correlation methods (the paper's own citation) prescribe. The report page then computes, live from all data collected so far:
- Pairwise Spearman correlations between the five rank orders (search, subjective, memorization, confusion, verbal) — the paper's Table 3.
- Kendall's coefficient of concordance (W) across the five rank orders — a measure of how much they agree, tie-corrected — the paper's Table 1, third step.
- An overall simplicity order, built the same way the paper built it: by summing each pattern's rank across the five experiments and re-ranking the sums — the paper's Table 2.
- The correlation between that overall order and each pattern's subsymmetry count — the paper's central result (Table 4), originally r = .808.