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bioRxivAnimal Behavior & CognitionPreprint

Topological structure in human spatial representation revealed through drawing

Mahwish Kittur, Agnes Zhang, Nessa V. Bryce, Sami R. YousifiD

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In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 3 (8 Oct 2026) · CC BY 4.0

When redrawing simple line figures from memory, adults and 5- to 8-year-olds pulled angles toward 90° yet kept T-junctions more often than L-junctions; adults also compressed length ratios.

Research on spatial representation has mostly emphasised Euclidean geometry, and studies of human topology have mostly examined object topology (rigid shapes with or without holes) using constrained experimental designs. Here, open-ended drawing from memory is used to probe network topology (T-junctions, crosses, holes) together with metric distortion of angles and lengths, in adults, serial-reproduction chains and young children.

Key results

  1. ShownAdults redrawing letter-like figures from memory systematically pulled angles toward 90°. The authors read this as precise angles not being encoded at all, rather than as a separate right-angle bias.

    Experiment 1 adults: 72.2% (SD 7.3%) of measured angles drawn closer to 90°, t(49)=21.64, p<.001, d=3.06; mean bias 12.07° (SD 3.20°), t(49)=26.68, p<.001, d=3.77; the pattern held for nine of ten stimuli. Experiment 3 final drawings after 10 serial reproductions: bias 17.07° (SD 16.55°), t(99)=10.32, p<.001, d=1.03. · Experiment 1: Angular distortions; Experiment 3: Serial Reproduction

  2. ShownT-junctions, which create a branch point, were reproduced with the correct count more often than visually similar L-junctions, which are topologically equivalent to a line. This replicated with a second stimulus set.

    Correct T- vs L-junction count, Experiment 1: 75% (SD 16.1%) vs 66% (SD 18.4%), t(49)=5.11, p<.001, d=.72. Experiment 2: 56.8% (SD 25.6%) vs 48.0% (SD 20.6%), t(49)=2.98, p=.004, d=.42. · Experiment 1: Angular distortions; Experiment 2: Length distortions

  3. ShownLine lengths were compressed toward a common value, and the compression grew when errors could build up along a serial-reproduction chain.

    Geometric mean of adjacent length ratios (true value 2.0): 1.89 (SD .24) for the Experiment 2 lines drawn in a 4:2:1 ratio, t(49)=3.62, p<.001, d=.51; 1.38 (SD .34) in the final drawings of Experiment 3 chains for the five stimuli designed with 2:1 length ratios, t(46)=8.11, p<.001, d=1.18 (3 of 50 chains dropped because coders could not agree). · Experiment 2: Length distortions; Experiment 3: Serial Reproduction; Experiment 2

  4. ShownAcross 10-person serial-reproduction chains, L-junctions were added or removed more often than T-junctions, and crosses changed least. In final drawings alone, the T- vs L-junction difference was only marginal.

    Per chain (100 chains, 1000 drawings): 2.04 (SD 2.197) L-junction vs 0.97 (SD 1.19) T-junction additions or removals, t(99)=4.71, p<.001, d=.47; crosses .22 (SD .58), fewer than T-junctions, t(99)=6.53, p<.001, d=.65. Final drawings only: T-junctions preserved in 46% vs L-junctions in 36% of sequences; mean .93 L- vs .74 T-junctions added or removed, t(99)=1.79, p=.076, d=.18. · Experiment 3: Serial Reproduction; Experiment 3

  5. ShownChildren aged 5 to 8 also biased angles toward 90° and preserved T-junctions more often than L-junctions. Age raised overall junction preservation but did not change the gap between the two junction types.

    126 children: 77.1% (SD 8.2%) of angles drawn closer to 90°, mean bias 14.01° (SD 4.49°), t(125)=35.05, p<.001; age predicted neither (p=.35, p=.70). Correct T- vs L-junction counts: 54.3% (SD 19.2%) vs 39.8% (SD 19.8%), p<.001, d=.77. Age predicted T (b=0.10) and L (b=0.094) preservation but not their difference (b=0.006, p=.72). · Experiment 4: Angular Distortions with Children; Experiment 4

Methods, data and reproducibility

Four preregistered drawing-from-memory experiments. Adults (recruited online) and children aged 5 to 8 viewed simple letter-like line figures, then redrew them on a digital canvas; one experiment chained 10 successive redrawings (serial reproduction). Two coders per drawing counted T- and L-junctions and measured angles and line-length ratios, which were then compared with the originals.

  • Experiment 1: adults recruited via Prolific (US residents fluent in English) redrawing ten letter-like figures (five with holes, equal T- and L-junction counts, no 90° angles) · human · n = 50 participants; two excluded
  • Experiment 2: new adult sample; ten hole-free figures, six with three lines in a 4:2:1 length ratio · human · n = 50 new participants; 7 additional excluded
  • Experiment 3: serial reproduction, 10 stages of 10 participants, stimuli taken from Experiments 1 and 2 · human · n = 100 participants; 1000 analyzable drawings; 97 exclusions replaced
  • Experiment 4: children aged 5 to 8 tested at the Museum of Life and Science, Durham, North Carolina (15 5-year-olds, 33 6-year-olds, 45 7-year-olds, 33 8-year-olds) · human · n = 126 children; 45 excluded
Methods & tools
Prolific, OSF, serial reproduction paradigm (Bartlett, 1932), online drawing canvas (600 x 600 pixels, mouse strokes), online angle measurement tool (unnamed)
Reproducibility gaps
No analysis code is mentioned. A six-person team coded the drawings by hand, measuring angles with an unnamed online tool. Preregistrations, stimuli, raw drawings and data are shared through an OSF view-only link.
Limitations (6)
  • In the serial-reproduction experiment, final drawings preserved T-junctions in 46% and L-junctions in 36% of sequences, and the difference in junctions added or removed (.93 L vs .74 T) was only marginal (p=.076). The authors note that L-junction additions and removals along a chain could cancel out. · stated by the authors
  • The authors describe the Experiment 1 and 2 biases as relatively subtle. That holes were almost never lost (<1%) was seen by inspecting the drawings but not analysed formally. · stated by the authors
  • The child sample was unbalanced: five-year-olds were underrepresented at the museum (15 of 126), 45 children were excluded, and the child procedure differed (self-paced study, no delay, experimenter could discard drawings, looser 60% exclusion rule). · stated by the authors
  • Measurements came from manual coding. In Experiment 3, 3 of 50 length chains were dropped because coders disagreed, and 97 participants with any unusable drawing were replaced to keep chains interpretable. · stated by the authors
  • The claim that children perform like adults is not backed by a direct child vs adult statistical test. Children's junction preservation (54.3% T, 39.8% L) is lower than adults' in Experiment 1 (75%, 66%), and the procedures differed between the groups. · noted in this summary
  • Two Experiment 4 tests are reported as t(49) even though 126 children were analysed (other Experiment 4 tests use t(125) or t(124)), so some reported statistics may be mislabelled. · noted in this summary

Read this if you study spatial cognition, shape or map representation, or cognitive development and want a preregistered, open-data drawing paradigm that tests topological features against metric angle and length information.

Citations
1

Abstract

Human spatial representations are often assumed to represent Euclidean properties such as length, distance, and angle. Here we test an alternative (but not mutually exclusive) possibility - that spatial memory is structured around topological relations. Across four experiments, adults and children memorized simple letter-like figures and reproduced them by drawing. Drawings showed systematic distortions of metric features, including strong biases of angles toward 90 degrees and compression of line length towards an average value. In contrast, topologically critical features - such as T-junctions and holes - were reliably preserved, even relative to closely matched but topologically irrelevant features like L-junctions. These effects were magnified in a serial reproduction paradigm, in which participants iteratively generated new drawings from previous participant drawings: At the end of each mnemonic chain, figures converged on simplified topological structures as metric detail degraded. Similar patterns were observed in children aged five to eight years. Together, these findings suggest that topological relations may function as primitive building blocks of human spatial representation, with metric detail encoded inconsistently.

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