research-document

ATLAS-0001: Proximity and Relative Separation

Research Area: General Research
Project: project-atlas
Useful for: integrate, verify
Audience: practitioner, researcher
Status: Evidence Review — Working Draft
Version: 0.1
Priority: medium
Tags: proximity, grouping, gestalt, spatial-organization, relative-separation, visual-perception, composition
Updated: 2026-07-22
Source: content/projects/project-atlas/research-note/atlas-0001-proximity-and-relative-separation-v0-1.md

ATLAS-0001: Proximity and Relative Separation

Purpose

This document asks a narrower and more useful question than whether proximity "is real":

What does existing research allow Project Atlas to claim about how spatial distance influences perceptual grouping, and what does it not yet justify?

Proximity is being used as the first reference implementation of the Atlas method. The objective is to demonstrate how published evidence becomes bounded observations, causal hypotheses, candidate laws, measurable variables, design implications, and open questions.

Key Findings

Closer elements are more likely to be grouped, but grouping is not governed by a universal hard distance threshold.
Relative distances among competing organizations matter more than an isolated absolute gap.
Grouping is probabilistic and can be multistable. A display may support more than one plausible organization, with perception shifting between them.
Proximity competes with other cues, including similarity, alignment, collinearity, connectedness, common region, orientation, and prior expectations.
Proximity may influence early organization faster than similarity under some cue-conflict conditions, but later processing can alter the final grouping judgment.
Perceptual grouping can affect attention and visual working memory, but benefits are conditional. Grouping can improve processing of included items while disadvantaging items excluded by the organization.
The current literature does not justify a universal CSS spacing token, pixel value, or single within-group/between-group ratio.

Scope and Terminology

Proximity

The tendency for spatially nearer elements to be perceived as belonging together.

Relative separation

The relationship between distances supporting one candidate grouping and the distances supporting competing groupings.

Candidate organization

Any plausible perceptual grouping supported by the geometry or other visual cues in a composition.

Multistability

A condition in which more than one organization is perceptually plausible and the perceived grouping may alternate.

Grouping judgment

A report of which elements appear to belong together. This is not equivalent to task performance, comprehension, memory, or interaction success.

Evidence Summary

EVD-PROX-001 — Quantitative proximity and multistability in dot lattices

Citation

Kubovy, M., & Wagemans, J. (1995). Grouping by proximity and multistability in dot lattices: A quantitative Gestalt theory. Psychological Science, 6(4), 225–234.

DOI: 10.1111/j.1467-9280.1995.tb00597.x

Evidence grade

Research contribution

The work developed a quantitative account of grouping in dot lattices where multiple orientations could support different organizations.

Direct finding

Grouping preference changes systematically with the relative distances that support competing lattice organizations.

Interpretation

This supports a probabilistic competition model rather than a binary rule. Proximity contributes evidence toward one organization, but alternative organizations remain possible when their spatial support is similar.

Supports

LAW-PROX-001: Relative Separation
LAW-PROX-002: Probabilistic Grouping
LAW-PROX-003: Competing Organization

Challenges

Any universal threshold stating that a particular gap always creates a group.
Any model treating grouping as a deterministic nearest-neighbor assignment.

Generalizability limits

Dot lattices are highly controlled and abstract.
Grouping reports do not directly measure interface task performance.
UI elements carry semantics, enclosure, typography, and interaction roles absent from simple dot patterns.

Source

https://doi.org/10.1111/j.1467-9280.1995.tb00597.x

EVD-PROX-002 — Century review of quantitative Gestalt research

Citation

Wagemans, J., Elder, J. H., Kubovy, M., Palmer, S. E., Peterson, M. A., Singh, M., & von der Heydt, R. (2012). A Century of Gestalt Psychology in Visual Perception I: Perceptual Grouping and Figure-Ground Organization. Psychological Bulletin, 138(6), 1172–1217.

DOI: 10.1037/a0029333

Evidence grade

Direct finding

The review documents the transition from qualitative Gestalt principles toward psychophysical and computational models in which grouping strength can be quantified and multiple cues can interact.

Interpretation

Proximity is best treated as one source of organization within a broader cue integration system. Its existence is well established, but its design translation remains conditional.

Supports

LAW-PROX-001: Relative Separation
LAW-PROX-002: Probabilistic Grouping
LAW-PROX-004: Cue Competition

Generalizability limits

A broad review establishes the state of perceptual science but does not supply a ready-made spacing specification for realistic interfaces.

Source

https://pmc.ncbi.nlm.nih.gov/articles/PMC3482144/

EVD-PROX-003 — Orientation and collinearity modify distance effects

Citation

Claessens, P. M. E., & Wagemans, J. (2008). Proximity, collinearity, and orientation priors in zigzag lattices. Perception.

PubMed ID: 19146265

Evidence grade

Direct finding

Perceptual grouping in zigzag lattices was not explained by distance alone. Cardinal and oblique organizations differed in their sensitivity to proximity and discollinearity.

Interpretation

The same geometric distance can carry different grouping strength depending on orientation and structural alignment. Distance is therefore not an independent or context-free variable.

Supports

LAW-PROX-004: Cue Competition
LAW-PROX-005: Orientation-Conditioned Proximity

Challenges

A one-dimensional spacing model.
Equal treatment of horizontal, vertical, diagonal, radial, and irregular arrangements.

Source

https://pubmed.ncbi.nlm.nih.gov/19146265/

EVD-PROX-004 — Proximity and similarity can have different temporal priority

Citation

Ben-Av, M. B., Sagi, D., & Braun, J. Perceptual grouping by similarity and proximity.

PubMed ID: 7740775

Evidence grade

Direct finding

Under cue conflict, proximity-based organization appeared earlier, while similarity could exert greater influence with additional processing time.

Interpretation

Spatial organization may make an early structural claim before color, shape, or semantic interpretation fully influences the percept.

Supports

LAW-PROX-004: Cue Competition
LAW-PROX-006: Temporal Cue Priority

Design implication

A layout whose spacing communicates the wrong structure should not rely on color alone to repair that structure, especially in brief, peripheral, or rapidly scanned presentations.

Source

https://pubmed.ncbi.nlm.nih.gov/7740775/

EVD-PROX-005 — Sequential processing of proximity and similarity

Citation

Johansson, R. C. G., et al. (2024). Serial processing of proximity groups and similarity groups in perceptual organization.

Evidence grade

Direct finding

The experiments indicated sequential rather than fully parallel processing under the tested conditions, with a temporal advantage for proximity grouping.

Interpretation

Cue strength is partly time-dependent. A final unlimited-viewing judgment may not describe the organization available during the first moments of perception.

Supports

LAW-PROX-006: Temporal Cue Priority
LAW-PROX-004: Cue Competition

Generalizability limits

The specific stimulus and task constrain the result.
The study does not establish that proximity always precedes every other cue.
Interface scanning includes learned expectations and semantic information.

Source

https://pmc.ncbi.nlm.nih.gov/articles/PMC11093805/

EVD-PROX-006 — Grouping can be influenced by top-down probability

Citation

Beck, D. M., & Palmer, S. E. (2002). Top-down influences on perceptual grouping. Journal of Experimental Psychology: Human Perception and Performance.

PubMed ID: 12421056

Evidence grade

Direct finding

Grouping was sensitive to the probability that a target pair would be organized by a particular cue when sufficient processing time was available. Effects differed in speed across grouping factors.

Interpretation

Perceptual grouping is not purely bottom-up. Learned expectation, task probability, and processing time can modify which organization dominates.

Supports

LAW-PROX-004: Cue Competition
LAW-PROX-007: Expectation-Conditioned Grouping

Challenges

The claim that proximity operates as an inflexible reflex.
Designs that assume geometric organization can be evaluated independently of user goals and learned conventions.

Source

https://pubmed.ncbi.nlm.nih.gov/12421056/

EVD-PROX-007 — Grouping can benefit visual working memory

Citation

Li, J., et al. (2018). Evidence for the beneficial effect of perceptual grouping on visual working memory. Scientific Reports.

Evidence grade

Direct finding

The work included an empirical study and a meta-analytic study examining whether perceptual grouping improves visual working-memory performance.

Interpretation

Grouping can alter effective encoding or maintenance, not merely visual appearance. However, the memory benefit depends on what features and relationships the grouping makes available.

Supports

LAW-PROX-008: Conditional Encoding Benefit
A broader Structural Encoding law

Generalizability limits

This evidence concerns perceptual grouping broadly, not proximity alone.
Memory benefit does not automatically imply faster navigation or better interaction.
Grouping may privilege some information at the expense of other information.

Source

https://pmc.ncbi.nlm.nih.gov/articles/PMC6138684/

EVD-PROX-008 — Proximity grouping extends beyond explicit visual reports

Citation

Overvliet, K. E., et al. (2013). Grouping by Proximity in Haptic Contour Detection.

Evidence grade

Direct finding

Closer proximity among contour elements increased detection rates and reduced exploration time in a haptic contour-detection task.

Interpretation

Proximity-based organization may reflect a broader perceptual strategy rather than a convention unique to visual graphic design.

Supports

A cross-modal proximity hypothesis
The possibility that proximity is a general organization mechanism

Generalizability limits

Haptic exploration is sequential and differs from visual perception.
Cross-modal similarity does not prove identical neural or computational mechanisms.
This cannot be translated directly into visual spacing guidance.

Source

https://pmc.ncbi.nlm.nih.gov/articles/PMC3676406/

Moderate to high

OBS-PROX-007 — Existing research does not validate universal interface bands

Observation

The strongest quantitative studies use dots, lattices, contours, or tightly controlled symbols rather than complete production interfaces.

Interpretation

It would be premature to publish rules such as:

internal gap must be exactly half the external gap;
8 pixels means related and 24 pixels means unrelated;
a ratio above a fixed value guarantees grouping.

Confidence

High

Candidate Laws

LAW-PROX-001 — Law of Relative Separation

Hypothesis

The probability that elements are perceived as a group rises as distances within that candidate group become smaller relative to distances supporting competing organizations.

Prediction

Holding element size and other cues constant, increasing the ratio of a competing gap to the intended within-group gap should increase reports of the intended organization.

Supporting evidence

EVD-PROX-001
EVD-PROX-002

Counter evidence

No evidence found that rejects the general relationship. However, orientation, similarity, semantic expectation, and other cues can reduce or override its effect.

Confidence

High as a perceptual relationship; low for any universal numeric threshold

LAW-PROX-002 — Law of Probabilistic Grouping

Hypothesis

Perceptual grouping represents a distribution over competing organizations rather than a deterministic classification.

Prediction

As two candidate organizations approach equal support, grouping judgments should become more variable and confidence should decline.

Supporting evidence

EVD-PROX-001
EVD-PROX-002

Supporting evidence

EVD-PROX-007

Confidence

Moderate to high for perceptual grouping generally; proximity-specific evidence remains incomplete

Provisional Mechanism Model

The earlier causal chain:

reduced distance
    → automatic grouping
    → reduced search area
    → reduced working-memory demand
    → faster recognition

is too simple.

A better provisional model is:

geometry and visual cues
    ↓
evidence for multiple candidate organizations
    ↓
time-dependent cue integration
    ↓
task- and expectation-conditioned grouping probability
    ↓
allocation of attention and encoding priority
    ↓
effects on search, memory, comprehension, and action

This model deliberately separates perceptual grouping from downstream outcomes. Grouping may influence search or memory, but it does not guarantee improvement.

Candidate Computational Representation

For each candidate organization G:

CueEvidence(G) =
    wp × relative_proximity
  + wa × alignment
  + wc × collinearity
  + ws × similarity
  + wr × common_region
  + wn × connectedness
  + wm × common_motion
  + we × semantic_expectation
  + wt × task_relevance

Then:

P(G) = exp(CueEvidence(G)) / Σ exp(CueEvidence(all candidate organizations))

Status

This is a conceptual architecture, not a fitted model.

What remains unknown

Valid weights for UI-like stimuli
Nonlinear cue interactions
Temporal changes in weights
Observer-specific priors
Effects of reading direction and culture
Effects of device, distance, and viewport
Whether task performance is predicted by subjective grouping probability

Measurement Model

MET-PROX-001 — Geometric relationship record

elements:
  width:
  height:
  shape:
  count:

distance:
  center_to_center_within:
  edge_to_edge_within:
  center_to_center_between:
  edge_to_edge_between:
  nearest_neighbor:
  repeated_distance_consistency:

ratios:
  between_to_within_center:
  between_to_within_edge:
  element_size_to_gap:
  horizontal_to_vertical:

candidate_organizations:
  rows:
  columns:
  sections:
  nested_groups:
  diagonals:
  semantic_units:

MET-PROX-002 — Competing cue record

alignment:
  strength:
  supports:

similarity:
  color:
  shape:
  size:
  typography:
  texture:
  supports:

boundaries:
  common_region:
  connectedness:
  divider:
  background:
  supports:

semantics:
  heading_association:
  label_value_relationship:
  learned_component_pattern:
  task_relationship:
  supports:

MET-PROX-003 — Viewing and task record

viewing:
  exposure_duration:
  viewing_distance:
  expected_fixation:
  eccentricity:
  viewport:
  scrolling:
  motion:

task:
  detect:
  identify:
  group:
  compare:
  read:
  remember:
  navigate:
  act:

outcomes:
  grouping_choice:
  grouping_confidence:
  reaction_time:
  accuracy:
  first_fixation:
  fixation_count:
  recall:
  task_completion:
  error_rate:

Composition Implications

Supported implications

1. Measure relationships, not isolated tokens

Record internal and external spacing together. A gap has meaning only relative to elements and alternatives around it.

2. Map plausible wrong groupings

A composition review should identify not only the intended grouping but every credible competing organization.

3. Treat spacing as an early structural cue

When spacing and color disagree, spacing may control the first percept even if color later changes the judgment.

4. Reinforce important structure with compatible cues

Spacing, alignment, headings, boundaries, and similarity should agree when misgrouping has meaningful consequences.

5. Do not maximize every cue

Over-reinforcement can fragment a layout, create excessive enclosure, or flatten hierarchy by making every boundary equally strong.

6. Distinguish perceptual success from task success

A layout can be grouped as intended yet remain difficult to read, compare, remember, or operate.

Unsupported implications

The current evidence does not support:

one universal proximity ratio for all layouts;
a universal pixel distance for grouping;
the claim that more whitespace is always better;
the claim that proximity always overrides similarity;
the claim that perceptual grouping automatically lowers cognitive load;
the claim that a visually neat composition is operationally effective.

Initial Atlas Design Diagnostic

Proximity Diagnostic v0.1

For each intended group:

What elements are intended to belong together?
What are the within-group center and edge distances?
What are the nearest competing distances?
Which alternative row, column, section, or semantic groupings are possible?
Which cues reinforce the intended organization?
Which cues contradict it?
Is the task performed during brief scanning or prolonged inspection?
Does the organization privilege the information users actually need?
Is the important relationship central or peripheral to expected fixation?
What observable outcome would demonstrate that the grouping works?

Evidence Sufficiency

Core perceptual claim

Rating: A

There is strong, replicated evidence that relative proximity influences visual grouping.

Quantitative interface translation

Rating: D

There is not yet enough direct evidence to define universal spacing bands for realistic interfaces.

Temporal interaction with similarity

Rating: C

Controlled studies support temporal differences, but generalization remains bounded.

Effects on task performance

Rating: C

Evidence indicates effects on attention and working memory, but interface-level task outcomes require more synthesis.

Need for original human experiments

Current priority: Low

Existing research is sufficient to build and refine the conceptual model. Original experiments should be deferred until the literature review identifies a narrow, consequential gap that cannot be answered from published data.

Open Questions

Which published studies provide recoverable psychometric functions relating spacing ratios to grouping probability?
How stable are proximity functions across dots, letters, icons, words, controls, cards, and mixed-content regions?
Should UI spacing be normalized by element size, center distance, edge gap, visual angle, or a combination?
How do nested groups alter the strength of local proximity?
When do semantic expectations override conflicting geometry?
How does reading direction change grouping preference?
How does responsive reflow affect learned grouping across viewport sizes?
Do grouping judgments predict task time, error rate, and memory in realistic interfaces?
Can computational vision estimate candidate organizations reliably enough to support an automated composition diagnostic?
What evidence distinguishes beneficial whitespace from empty space that weakens continuity, comparison, or information density?

Next Actions

Retrieve and extract quantitative details from the Kubovy and Wagemans dot-lattice studies.
Build a source table of proximity-versus-similarity cue-conflict experiments.
Separate evidence into:
- grouping judgment,
- visual search,
- attention,
- working memory,
- task performance.
Identify studies using text, symbols, diagrams, or interface-like stimuli.
Create a machine-readable evidence JSON schema matching this document.
Apply the Proximity Diagnostic to several existing layouts as case studies, without treating those case studies as scientific proof.

Revision History

Version	Date	Author	Summary
0.1	2026-07-18	Kevin Miller and ChatGPT	First formal Atlas principle review. Synthesized proximity evidence, created candidate laws, measurement records, a provisional mechanism model, design boundaries, and a targeted research backlog.

Agent Instructions

When creating or modifying this document:

Separate direct observation from interpretation.
Never strengthen a conclusion beyond the available evidence.
Preserve contradictory findings and moderator variables.
Prefer measurable relationships over subjective descriptions.
Reference stable IDs for observations, evidence, laws, and metrics.
Do not convert laboratory distances directly into pixel recommendations.
Do not treat perceptual grouping as synonymous with usability.
Record the stimulus, task, population, viewing conditions, and outcome.
Retain prior revisions and append changes to the revision history.
Mark computational equations as provisional until fitted and validated.