A shared fractal aesthetic across development

The study investigates how aesthetic preferences for fractal patterns vary with fractal complexity and whether these preferences are shared across development from early childhood to adulthood. Fractal complexity is governed by recursion and fractal dimension D, and is influenced by the character of repetition (statistical vs exact) and spatial symmetry. Prior work shows preference peaks at low-to-moderate complexity for statistical fractals common in nature, while exact fractals—characterized by symmetry and precise recursion—are preferred at higher complexities. The research question asks whether these established adult trends also appear in children, and whether individual differences in processing style (systemizing tendencies and susceptibility to the Ponzo illusion indicating local/global bias) relate to complexity preferences. This has implications for the Fractal Fluency theory, which posits the visual system is tuned to common natural fractal complexities, with potential benefits for designing naturalistic built environments. The study tests a wide age range (3–10-year-old children and adults) to determine developmental stability of fractal preferences and examines individual differences using the Systemizing Quotient (SQ) and Ponzo task.

• Aesthetic preference depends on fractal complexity and pattern type. Statistical fractals prevalent in natural scenery elicit peak preference at low-moderate D (≈1.3–1.4 on a 1.1–1.9 range), with decreasing preference at higher complexity. Jackson Pollock’s paintings exhibit fractal structure; cropped black-and-white versions show peak preference at mid-complexity. Fractal properties occur broadly in traditional and contemporary art across cultures, suggesting universal tendencies, with subgroups showing different preferred D values. Analyses suggest preference for lower D with certain age-related neurological conditions (e.g., Alzheimer’s, Parkinson’s).
• Exact fractals with symmetry and precise recursion increase tolerance for complexity, shifting preferred D to higher values.
• Fractal Fluency theory: repeated exposure or evolutionary tuning to natural low-moderate D patterns enhances processing fluency and preference; unnatural Euclidean patterns can induce visual discomfort and lower preference. Naturalistic fractal installations can reduce stress in built environments.
• Developmental and individual differences: susceptibility to contextual illusions varies with development; local/global processing biases may influence preference for fine-scale (high D) vs large-scale (low-mid D) structure. The Goldilocks effect predicts attention/preference for information of intermediate complexity that matches current processing capacity, potentially shifting with age. Systemizing tendencies (SQ) and susceptibility to global context effects (Ponzo illusion) relate to processing style and could modulate complexity preferences. Prior work reports wide effect sizes in preference tasks and suggests potential subgroup differences.

Participants: 178 total participants were recruited (University of Oregon students and Eugene Science Center visitors). Adults: 82 retained (of 83 tested), 75 females, ages 18–40 (reported as 18–33 retained), mean age ~20; recruited via SONA, received course credit. Children: 96 retained (of 118 tested), ages 3–10, 43 females, mean age 6.5; approximately equal male/female distribution across age bands 3–4, 5–6, 7–8, 9–10; received stamps/stickers. Informed consent followed IRB-approved protocols; parental consent and child assent for minors.

Apparatus: Fractal and Ponzo tasks presented on a Microsoft Surface Pro touchscreen tablet (~25 cm viewing distance). Adult questionnaires (including SQ) on an iPad; parents completed children’s SQ while children performed tasks.

Stimuli: Four fractal stimulus sets: two statistical and two exact. Exact sets: exact midpoint displacement fractals (algorithm per Fournier et al., 1982; Bies et al., 2016a,b) and H-tree exact fractals (repeating H-pattern). Statistical sets: midpoint-displacement variants (two different seeds). Each set had five D-values: 1.1, 1.3, 1.5, 1.7, 1.9 (lower D = less complex). Statistical fractals repeat statistical properties across scale; exact fractals repeat precisely with symmetry.

Design and Procedure: Between-subjects factor: Fractal-Type (statistical vs exact); between-subjects factor: Age (children 3–10 vs adults 18+). Within-subjects factor: D-value (five levels). Each participant completed two randomized blocks, each with one stimulus set (either one of the two exact sets or one of the two statistical sets), with three practice trials using different stimuli preceding each task. In each block, participants completed a two-alternative forced choice (2AFC) preference task comprising 10 trials, each presenting a pair of fractals of different D-values; all pairwise D-value combinations appeared once per block. Constraints: each D appeared four times per block; side with higher complexity counterbalanced; each D appeared on both left and right. A touchable fixation (smiley face) advanced trials. Participants indicated the preferred image by touching it.

Ponzo Task: After preference tasks, participants completed 10 trials of a Ponzo illusion task: two slanted vertical lines created converging context; two horizontal lines (upper target, lower adjustable) appeared between them; the lower line was adjusted via touch to match the upper line’s length. Accuracy recorded as pixel error (difference between adjusted and target lengths) and direction of bias (over/underestimation).

Questionnaires: Adults completed demographic items and the Systemizing Quotient (SQ; 0–150 range). Parents/guardians completed the children’s SQ (shorter; 0–56 range) while children performed tasks.

Data exclusion: Of 83 adults and 118 children tested, retained data for 82 adults and 96 children after excluding for incomplete participation, failure to comprehend instructions, or poor focus.

Analyses: Fractal preference analyzed as the proportion of choices per D-value in 2AFC comparisons. Mixed ANOVAs: 5×2×2 (D-value × Age × Fractal-Type) for full sample; Greenhouse–Geisser corrections applied when sphericity violated. Additional 5×4×2 mixed ANOVA for child subgroups (age bands). Planned paired-samples t-tests compared D-value levels within Fractal-Type; independent-samples t-tests compared exact vs statistical at each D. Ponzo errors and SQ scores compared across age via t-tests; SQ standardized across adult/child scales; Ponzo errors log-transformed for normality. Correlations assessed relationships between SQ and Ponzo error overall and within adults. Multiple linear regressions predicted preference from Fractal-Type, D-value, their interaction (Step 1), then adding SQ and Ponzo error (Step 2); an adult-only regression examined SQ and Ponzo error predicting adult preference. Statistical software: IBM SPSS Statistics 25 for Mac.

• Fractal preference ANOVA (5×2×2): Significant main effect of D-value (F(2.08, 362.67)=3.79, p≈0.02, ηp²=0.02). No main effects of Age (F(1,174)=0.001, p=0.97, ηp²<0.001) or Fractal-Type (F(1,174)=2.13, p=0.15, ηp²=0.01). Significant D-value × Fractal-Type interaction (F(2.08,362.67)=2.94, p≈0.05, ηp²=0.02). No interactions involving Age.
• Child-only ANOVA (5×4×2): No main effects of D-value, age band, or Fractal-Type; significant D-value × Fractal-Type interaction (F(2.54,223.28)=3.49, p=0.02, ηp²=0.04). No higher-order interactions.
• Preference trends: Statistical fractals peaked at low–moderate complexity; highest mean preference at D=1.3 (M=0.23, SD=0.09) vs D=1.1 (M=0.18, SD=0.12), t(85)=-4.55, p<0.001, d=0.45; D=1.3 > D=1.9 (M=0.18, SD=0.14), t(85)=2.03, p=0.046, d=0.41; D=1.7 (M=0.21, SD=0.09) > D=1.9, t(85)=2.26, p=0.027, d=0.24. For exact fractals, preference increased with D: D=1.1 (M=0.17, SD=0.11) < D=1.5 (M=0.21, SD=0.07), t(91)=-2.83, p=0.006, d=0.44; D=1.1 < D=1.7 (M=0.22, SD=0.09), t(91)=-2.73, p=0.008, d=0.49; D=1.1 < D=1.9 (M=0.22, SD=0.11), t(91)=-2.59, p=0.011, d=0.48; D=1.3 (M=0.18, SD=0.08) < D=1.5, t(91)=-2.15, p=0.034, d=0.32; D=1.3 < D=1.7, t(91)=-2.11, p=0.038, d=0.38.
• Exact vs statistical by D: Significant differences at D=1.3 (exact lower, M=0.18 vs statistical M=0.23), t(176)=-3.30, p<0.001, d=0.52; and D=1.9 (exact higher, M=0.22 vs statistical M=0.18), t(159.28)=2.18, p=0.030, d=0.32. Other D values not significant.
• Age effects: No Age × D interaction; children and adults showed similar preference patterns.
• Individual differences: Ponzo error overall M=33.24 pixels (SD=37.11); adults M=24.82 (SD=24.38), children M=41.66 (SD=45.09); adults more accurate than children, t(162)=-4.91, p<0.001, d=-0.77. Standardized SQ: adults mean 63.7 (SD=20.68; 0–150 scale), children mean 25 (SD=8.15; 0–56 scale); no age difference in standardized SQ, t(109)=0, p=1.0, d=0.00. Overall SQ–Ponzo correlation not significant (r=-0.12, p=0.22). Adult-only: significant negative correlation r=-0.21, p=0.028 (higher SQ associated with lower Ponzo error).
• Regression predicting preference: Step 1 (Fractal-Type, D, interaction) significant, F(3,886)=5.98, p<0.001, R²=0.02. Step 2 adding SQ and Ponzo error not significant, F(5,519)=0.66, p=0.66, R²=0.01; neither SQ nor Ponzo error contributed. Adult-only regression (SQ, Ponzo error): F(2,407)=0.00, p=0.99, R²<0.001; no predictive value.
• Overall pattern: Statistical fractal preference peaks at low–moderate D (≈1.3) and declines at higher D; exact fractal preference increases with D, peaking at higher complexities; these trends are consistent in children and adults.

The findings confirm robust, distinct preference profiles for statistical versus exact fractals: statistical fractals, common in natural environments, elicit maximal preference at low-to-moderate complexities, whereas exact fractals with symmetry and precise recursion are increasingly preferred at higher complexities. Crucially, the absence of age effects or Age × D interactions indicates that these aesthetic preferences are already present by early childhood and remain stable through adulthood. This developmental stability supports the Fractal Fluency account that the visual system is tuned—through evolutionary pressures and/or early exposure—to efficiently process the low-to-moderate complexity structures prevalent in nature. While individual differences in processing style were measurable (adult SQ negatively correlated with Ponzo error), they did not explain variance in fractal preference, suggesting that fractal aesthetic preferences may be broadly universal and relatively independent of local/global processing biases as captured by SQ and the Ponzo illusion. These results have implications for designing visual environments: incorporating naturalistic low-to-moderate D statistical fractals may optimize comfort and aesthetic experience across age groups, supporting stress-reduction and visual comfort in built spaces.

This study provides the first direct comparison of aesthetic preferences for statistical versus exact fractals across development, demonstrating that both children and adults show the canonical preference patterns: statistical fractals are preferred at low-to-moderate complexity, while exact fractals are preferred at higher complexity. The lack of age effects suggests an early-emerging, shared fractal aesthetic consistent with Fractal Fluency. Individual differences in systemizing tendencies and susceptibility to the Ponzo illusion did not predict fractal preferences. Future research should (a) extend to earlier developmental stages (infancy to 3 years) to pinpoint the onset and shaping of fractal fluency, (b) increase sample sizes and reduce attrition to better evaluate individual differences, and (c) further explore subgroup preferences and potential modulators (e.g., cultural exposure, neurodiversity) across the lifespan to optimize applications in naturalistic and built environments.

• Effect sizes for preference ANOVAs were small, consistent with some prior preference research, but they limit the strength of inferences.
• Child data experienced attrition, particularly for Ponzo and SQ measures (due to task comprehension and lack of parental questionnaire completion), reducing power for individual-differences analyses.
• Reported p-values contain minor formatting anomalies (e.g., p=0.02%), though significance interpretations align with conventional thresholds.
• Ponzo errors required log transformation due to non-normality; children’s distributions may have been especially affected by attrition and comprehension variability.
• The SQ adult and child versions differ in length/scales; although standardized, scale differences and reduced child data may have obscured relationships.
• Stimuli were limited to two exact and two statistical seeds with five discrete D-values; broader stimulus sets might reveal finer-grained effects.
• Cross-sectional design cannot disentangle developmental causality from early-established preferences due to evolution or early exposure.