Card Sorting & Information Architecture Simulator

Synthetic Card Sort

Participants 20

Sorting consistency 70%

Clusters shown (K) 4

Live Readouts

Avg. pairwise similarity

Purity vs. true topics

Merge height at K cut (avg. distance)

0.00

Cluster Colors

How it works

Each of the 15 cards has a hidden "true" topic. Every synthetic participant sorts all 15 cards into piles: with probability equal to the consistency slider they keep a card in its true topic, otherwise they drop it into a random other topic — modelling the disagreement real open card-sort studies always show.

sim(i,j) = (# participants who put i and j
            in the same pile) / N participants
dist(i,j) = 1 - sim(i,j)

Average-linkage agglomerative clustering repeatedly merges the two card groups whose members are, on average, least dissimilar:

merge(A,B) = argmin  1/(|A||B|) · Σ dist(a,b)
                A,B          a∈A, b∈B

Cutting that merge tree at K clusters (the slider) recovers an information architecture straight from user behaviour, without anyone hand-designing a menu. Purity checks how much of that emergent structure matches the 4 hidden topics; merge height is the dissimilarity of the last merge needed to reach K groups — low means the K clusters are clean and well separated.

The 3D layout is a physical simulation, not a static diagram: every pair of cards repels like charges (F ∝ 1/d²) while a spring pulls each pair toward a rest length proportional to dist(i,j) (F = k·(d − d_target)). Cards that many participants grouped together end up close together on screen; cards that were rarely paired drift apart.

Real-world relevance: this is exactly how UX researchers turn raw open/closed card-sort data (via tools like Optimal Workshop) into a website's navigation and category structure.

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