Universal fractality of morphological transitions in stochastic growth processes
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Summary
This work introduces two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth and shows that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics.
- Type
- article
- Published
- 2017-06-14
- Cited by
- 11
- References
- 35
- Access
- Open access
- OpenAlex
- https://openalex.org/W2622083389
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:38312546
Keywords
Computer science, Statistical physics, Physics
References
- Toward Self-Organization and Complex Matter
- Fluctuations and Scaling in Biology
- Fractals, scaling, and growth far from equilibrium
- Fractals in physiology and medicine.
- Tip splittings and phase transitions in the dielectric breakdown model: mapping to the diffusion-limited aggregation model.
- Growth and forms of Laplacian aggregates.
- Fractal dimensionality for the eta model.
- Theory of fractal growth.
- Effects of random-walk size on the structure of diffusion-limited aggregates.
- A theory of fractal dimensionality for generalized diffusion-limited aggregation
- Diffusion-limited aggregation: A kinetic critical phenomenon?
- The universality class of diffusion-limited aggregation and viscous fingering
- Fractal Dimension of Dielectric Breakdown
- Evidence of critical behavior in a random fractal automaton.
- From snowflake formation to growth of bacterial colonies II: Cooperative formation of complex colonial patterns
- Fractal to nonfractal phase transition in the dielectric breakdown model.
- Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation
- From snowflake formation to growth of bacterial colonies
- Cluster-particle aggregation with fractal (Levy flight) particle trajectories
- Universality of critical screening in the formation of fractal patterns
Cited by
- The fractal dimensions of Laplacian growth: an analytical approach based on a universal dimensionality function
- Angular and radial correlation scaling in stochastic growth morphodynamics: a unifying fractality framework
- From octopus to dendrite-Semiflexible polyelectrolyte brush condensates in trivalent counterion solution.
- A universal dimensionality function for the fractal dimensions of Laplacian growth
- The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics
- Features of Self-Organization of Objects with a Fractal Structure of Dendritic Geometry
- Network efficiency of spatial systems with fractal morphology: a geometric graphs approach
- Diffusion limited aggregation, resetting and large deviations of Brownian motion
- Angular and radial density correlation scaling in stochastic growth morphodynamics : a unifying fractality framework
- Space microgravity enhanced fractal dendrite coverage on solidifying alloy droplet surface
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