ArticleScientific reports2017
Definition of fractal topography to essential understanding of scale-invariance.
Article in Scientific reports, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- Wobble-board instability re-orthogonalizes postural geometry in older adults through exogenous constraint.GeroScience · 2026Article
- Microscopic Insight into Knudsen and Electromagnetic Effects on Thermal Conductivity of Closed Mesoporous Metal Gels.Gels (Basel, Switzerland) · 2025Article
- Fractal-Based Thermal Conductivity Prediction Modeling for Closed Mesoporous Polymer Gels.Gels (Basel, Switzerland) · 2025Article
- A fractal gripper with switchable mode for geometry adaptive manipulation.Scientific reports · 2025Article
- Angular distribution of fractal temporal correlations supports adaptive responses to wobble board instability.Journal of the Royal Society, Interface · 2025Article
- Older adults and individuals with Parkinson's disease control posture along suborthogonal directions that deviate from the traditional anteroposterior and mediolateral directions.Scientific reports · 2024Article
- Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation.Frontiers in network physiology · 2024Article
- Spatial variability and directional shifts in postural control in Parkinson's disease.Clinical parkinsonism & related disorders · 2024Article
- Prebiotic Aggregates (Tissues) Emerging from Reaction-Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension.Entropy (Basel, Switzerland) · 2022Article
- Chaos game representation and its applications in bioinformatics.Computational and structural biotechnology journal · 2021Review
- Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories.Scientific reports · 2020Article
- Fractal conceptualization of intumescent fire barriers, toward simulations of virtual morphologies.Scientific reports · 2019Article
Corrections and comments
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Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter H
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.