Fractal growth processes
NaturePublished 1 August 1986Open access
Leonard M. Sander
Citations320
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
The methods of fractal geometry allow the classification of non-equilibrium growth processes according to their scaling properties. This classification and computer simulations give insight into a great variety of complex structures.
Keywords
Computer ScienceEarth and Planetary SciencesPhysics and Astronomy
American Journal of Physics<i>The Fractal Geometry of Nature</i>
21,750 Citations1983Benoît B. Mandelbrot, John Wheeler
Journal of the Royal Statistical Society Series A (General)The Fractal Geometry of Nature.
14,691 Citations1984Colin Sparrow, B. B. Mandelbrot
Physica D Nonlinear PhenomenaMeasuring the strangeness of strange attractors
5,643 Citations1983Peter Grassberger, Itamar Procaccia
Physical Review LettersDynamic Scaling of Growing Interfaces
5,441 Citations1986Mehran Kardar, Giorgio Parisi +1 more
A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.
Physical Review LettersDiffusion-Limited Aggregation, a Kinetic Critical Phenomenon
5,307 Citations1981Thomas A. Witten, Leonard M. Sander
Princeton University Press eBooksOn Growth and Form, 1917
4,218 Citations2019D’Arcy Wentworth Thompson
Reviews of Modern PhysicsInstabilities and pattern formation in crystal growth
2,596 Citations1980J. S. Langer
Physical review. A, General physicsErratum: Fractal measures and their singularities: The characterization of strange sets [Phys. Rev. A<i>33</i>, 1141 (1986)]
2,482 Citations1986Thomas C. Halsey, Mogens H. Jensen +3 more
Journal of Applied PhysicsMorphological Stability of a Particle Growing by Diffusion or Heat Flow
2,000 Citations1963W. W. Mullins, Robert F. Sekerka
Journal of Fluid MechanicsIntermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
1,874 Citations1974Benoît B. Mandelbrot
Physical review. B, Condensed matterDiffusion-limited aggregation
1,830 Citations1983Thomas A. Witten, Leonard M. Sander
Physica D Nonlinear PhenomenaThe infinite number of generalized dimensions of fractals and strange attractors
1,802 Citations1983H. G. E. Hentschel, Itamar Procaccia
PhysicaOn the random-cluster model
1,772 Citations1972C.M. Fortuin, Piet Kasteleyn
It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.
Physical Review LettersFormation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation
1,618 Citations1983Paul Meakin
Physical Review LettersFractal Dimension of Dielectric Breakdown
1,603 Citations1984L. Niemeyer, L. Pietronero +1 more
Journal of Physics A Mathematical and GeneralScaling of the active zone in the Eden process on percolation networks and the ballistic deposition model
1,505 Citations1985Fereydoon Family, Tamás Vicsek
Physical Review LettersScaling of Kinetically Growing Clusters
1,051 Citations1983M. Kolb, Robert Botet +1 more
Physical Review LettersFractal Structures Formed by Kinetic Aggregation of Aqueous Gold Colloids
907 Citations1984D. A. Weitz, M.C. Oliveria
Physical Review LettersFractal Geometry of Colloidal Aggregates
743 Citations1984Dale W. Schaefer, James E. Martin +2 more
Physical Review LettersFractal Structures of Zinc Metal Leaves Grown by Electrodeposition
703 Citations1984Mitsugu Matsushita, Masaki Sano +3 more
Physical Review LettersLimits of the Fractal Dimension for Irreversible Kinetic Aggregation of Gold Colloids
690 Citations1985David A. Weitz, J. S. Huang +2 more
On montre qu'il existe 2 regimes d'agregation cinetique, irreversible, de colloides aqueux, determinee par le potentiel interparticulaire a courte distance, avec controle de la probabilite de collage lors de l'approche de 2 particules.
Scaling Phenomena in Disordered Systems
657 Citations1991R. Pynn, A. T. Skjeltorp
NatureFractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon
618 Citations1985J. Nittmann, Gérard Daccord +1 more
Physical review. A, General physicsBallistic deposition on surfaces
611 Citations1986Paul Meakin, P. Ramanlal +2 more
The ballistic aggregation model, in which particles are added to a growing structure via linear (ballistic) trajectories, is the most fundamental of these models and has been studied intensively.
Physical Review LettersDendritic and Fractal Patterns in Electrolytic Metal Deposits
556 Citations1986Yasuji Sawada, Andrew Dougherty +1 more
Most strikingly, a transition from dendritic crystals (where crystalline anisotropy dominates) to disordered ramified patterns is found when the electrolyte concentration is reduced.
Physical Review LettersMorphology and Microstructure in Electrochemical Deposition of Zinc
518 Citations1986David G. Grier, Eshel Ben‐Jacob +2 more
A previously unrecognized transition region between diffusion-limited aggregation and dendritic growth is reported and analysis of the microstructure suggests mechanisms for the macroscopic expression of crystalline anisotropy.
Physical Review LettersDiffusion-Limited Aggregation and Two-Fluid Displacements in Porous Media
455 Citations1984Lincoln Paterson
Physical Review LettersExperimental Demonstration of the Role of Anisotropy in Interfacial Pattern Formation
418 Citations1985Eshel Ben‐Jacob, R. Godbey +5 more
Physical Review LettersScaling structure of the surface layer of diffusion-limited aggregates
386 Citations1986Thomas C. Halsey, Paul Meakin +1 more
NatureTip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy
386 Citations1986J. Nittmann, H. Eugene Stanley
Physical Review LettersPore-Scale Viscous Fingering in Porous Media
351 Citations1985Jing‐Den Chen, David Wilkinson
Physical Review LettersPattern Formation in Diffusion-Limited Aggregation
278 Citations1984Tamás Vicsek
Physical review. A, General physicsGeometrical models of interface evolution
266 Citations1984Richard C. Brower, David A. Kessler +2 more
Physical Review LettersOccupancy-Probability Scaling in Diffusion-Limited Aggregation
253 Citations1985Leonid A. Turkevich, H. Scher
A continuous-time random-walk theory of diffusion-limited aggregation yields perimeter occupancy probabilities that agree with the analytic probabilities near cusps of a lattice-symmetric array of traps.
Physical Review LettersActive Zone of Growing Clusters: Diffusion-Limited Aggregation and the Eden Model
238 Citations1984Michael Plischke, Zoltàn Ràcz
Physical review. A, General physicsDiffusion-controlled deposition on fibers and surfaces
231 Citations1983Paul Meakin
Journal of Physics A Mathematical and GeneralHierarchical model for chemically limited cluster-cluster aggregation
206 Citations1984R. Jullien, M. Kolb
A hierarchical model is introduced to describe chemically limited cluster-cluster aggregation and an exponent characterising the number of active sites per cluster are evaluated numerically for d=2,3,4.
Physical review. A, General physicsScaling properties for the surfaces of fractal and nonfractal objects: An infinite hierarchy of critical exponents
196 Citations1986Paul Meakin, Antonio Coniglio +2 more
Physical review. A, General physicsBoundary-layer model of pattern formation in solidification
195 Citations1984Eshel Ben‐Jacob, Nigel Goldenfeld +2 more
Physical review. A, General physicsSingularities in nonlocal interface dynamics
192 Citations1984Boris I. Shraiman, David Bensimon
Physical review. A, General physicsDiffusion-limited aggregation and the Saffman-Taylor problem
189 Citations1985Chao Tang
A random-walk model is proposed to simulate Darcy-law two-dimensional flows in hydrodynamics in the limit of zero-surface tension and it is clear that the mean-field .limit of diffusion-limited aggregation is a Saffman-Taylor problem.
Journal of Statistical PhysicsSimulating hydrodynamics: A pedestrian model
188 Citations1985Leo P. Kadanoff
Journal of Physics A Mathematical and GeneralSize distribution of clusters in irreversible kinetic aggregation
149 Citations1984Robert Botet, R. Jullien
Physical Review LettersAnisotropy and Cluster Growth by Diffusion-Limited Aggregation
136 Citations1985R. C. Ball, Robert M. Brady +2 more
A simple theory of diffusion-limited-aggregation cluster growth which relates the large-scale shape of the cluster to its fractal dimension and results of computer simulation for DLA clusters grown with anisotropic sticking rules are presented.
Physical review. A, General physicsCausality bound on the density of aggregates
120 Citations1984R. C. Ball, Thomas A. Witten
Journal of Physics A Mathematical and GeneralHierarchical model for irreversible kinetic cluster formation
119 Citations1984Robert Botet, R. Jullien +1 more
A model to describe the growth of clusters by a mechanism of irreversible clustering of clusters is proposed, which looks like the diffusion limited aggregation model, which for the sake of comparison is treated by the same renormalisation-group method.
Journal of Physics A Mathematical and GeneralLarge scale lattice effect in diffusion-limited aggregation
117 Citations1985R. C. Ball, R. Michael Brady
Physical review. B, Condensed matterEffects of particle drift on diffusion-limited aggregation
108 Citations1983Paul Meakin
Physical Review LettersComment on "Active Zone of Growing Clusters: Diffusion-Limited Aggregation and the Eden Model"
100 Citations1985Paul Meakin, L. M. Sander
Physical review. A, General physicsDiffusion-limited aggregation as a deterministic growth process
91 Citations1985L. M. Sander, P. Ramanlal +1 more
A set of deterministic continuum equations is proposed to represent diffusion-limited aggregation that gives growth very similar to discrete simulations and the relationship to viscous fingering and other growth processes is explored.
Physica A Statistical Mechanics and its ApplicationsDiffusion limited aggregation and its response to anisotropy
87 Citations1986R. C. Ball
Physical review. A, General physicsStructure of large two-dimensional square-lattice diffusion-limited aggregates: Approach to asymptotic behavior
86 Citations1987Paul Meakin, R. C. Ball +2 more
The results are consistent with an asymptotic (scaling) fractal geometry for square-lattice DLA but suggest that these fractals are neither self-similar nor homogeneous.
Physical review. A, General physicsGrowth of fractal crystals in amorphous<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">GeSe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>films
71 Citations1987Gy. Radnóczi, Tamás Vicsek +2 more
The first study of fractal growth in a solid-solid phase transition is presented, obtained by heating thin amorphous GeSe films and the result for the fractal dimension is in agreement with that of two-dimensional diffusion-limited aggregates.
Physical review. A, General physicsActive zone of growing clusters: Diffusion-limited aggregation and the Eden model in two and three dimensions
62 Citations1985Zoltàn Ràcz, Michael Plischke
On trouve qu'il faut etre tres attentif aux simulations de l'agregation limitee par diffusion, car un certain nombre de particules peuvent conduire a un mouvement qui peut masquer la structure intrinseque des agregats.
Physical review. A, General physicsDiverging length scales in diffusion-limited aggregation
60 Citations1986Paul Meakin, Fereydoon Family
Physical Review LettersSome consequences of an equation of motion for diffusive growth
58 Citations1987Thomas C. Halsey
Physics Letters AOn the ballistic model of aggregation
49 Citations1984David Bensimon, Boris I. Shraiman +1 more
Physical review. B, Condensed matterCrossover in diffusion-limited aggregation
45 Citations1983Michael Nauenberg, R. Richter +1 more
Journal of Statistical PhysicsParticle aggregation versus cluster aggregation in high dimensions
44 Citations1984R. C. Ball, Thomas A. Witten
This work shows that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD0 of the aggregate, and presents a soluble model that should agree with Sutherland's binary aggregation model in high dimensions.
Journal of Colloid and Interface ScienceComputer simulations of soot aggregation
39 Citations1984Roy Richter, Leonard M. Sander +1 more
Analysis by visual means, calculation of bond order, and correlation functions indicate that the physically reasonable models proposed so far do not reproduce some aspects of observed soot aggregates, such as the long chains seen by Stevenson.
Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsComment on "Quantum dynamics of Kaluza-Klein theories"
17 Citations1984Daniel Rohrlich
