scispace - formally typeset
Search or ask a question
Topic

Fractal

About: Fractal is a research topic. Over the lifetime, 27333 publications have been published within this topic receiving 535436 citations. The topic is also known as: fractals & fractal set.


Papers
More filters
Book
01 Jan 1985
TL;DR: In this paper, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
Abstract: Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in disordered media Coming attractions Further reading Cluster Numbers The truth about percolation Exact solution in one dimension Small clusters and animals in d dimensions Exact solution for the Bethe lattice Towards a scaling solution for cluster numbers Scaling assumptions for cluster numbers Numerical tests Cluster numbers away from Pc Further reading Cluster Structure Is the cluster perimeter a real perimeter? Cluster radius and fractal dimension Another view on scaling The infinite cluster at the threshold Further reading Finite-size Scaling and the Renormalization Group Finite-size scaling Small cell renormalization Scaling revisited Large cell and Monte Carlo renormalization Connection to geometry Further reading Conductivity and Related Properties Conductivity of random resistor networks Internal structure of the infinite cluster Multitude of fractal dimensions on the incipient infinite cluster Multifractals Fractal models Renormalization group for internal cluster structure Continuum percolation, Swiss-cheese models and broad distributions Elastic networks Further reading Walks, Dynamics and Quantum Effects Ants in the labyrinth Probability distributions Fractons and superlocalization Hulls and external accessible perimeters Diffusion fronts Invasion percolation Further reading Application to Thermal Phase Transitions Statistical physics and the Ising model Dilute magnets at low temperatures History of droplet descriptions for fluids Droplet definition for the Ising model in zero field The trouble with Kertesz Applications Dilute magnets at finite temperatures Spin glasses Further reading Summary Numerical Techniques

9,830 citations

Book
01 Jan 1992
TL;DR: In this article, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
Abstract: Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in disordered media Coming attractions Further reading Cluster Numbers The truth about percolation Exact solution in one dimension Small clusters and animals in d dimensions Exact solution for the Bethe lattice Towards a scaling solution for cluster numbers Scaling assumptions for cluster numbers Numerical tests Cluster numbers away from Pc Further reading Cluster Structure Is the cluster perimeter a real perimeter? Cluster radius and fractal dimension Another view on scaling The infinite cluster at the threshold Further reading Finite-size Scaling and the Renormalization Group Finite-size scaling Small cell renormalization Scaling revisited Large cell and Monte Carlo renormalization Connection to geometry Further reading Conductivity and Related Properties Conductivity of random resistor networks Internal structure of the infinite cluster Multitude of fractal dimensions on the incipient infinite cluster Multifractals Fractal models Renormalization group for internal cluster structure Continuum percolation, Swiss-cheese models and broad distributions Elastic networks Further reading Walks, Dynamics and Quantum Effects Ants in the labyrinth Probability distributions Fractons and superlocalization Hulls and external accessible perimeters Diffusion fronts Invasion percolation Further reading Application to Thermal Phase Transitions Statistical physics and the Ising model Dilute magnets at low temperatures History of droplet descriptions for fluids Droplet definition for the Ising model in zero field The trouble with Kertesz Applications Dilute magnets at finite temperatures Spin glasses Further reading Summary Numerical Techniques

7,349 citations

Book
16 Mar 1990
TL;DR: In this article, a mathematical background of Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractality products of fractal intersections of fractalities.
Abstract: Part I Foundations: mathematical background Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractals products of fractals intersections of fractals. Part II Applications and examples: fractals defined by transformations examples from number theory graphs of functions examples from pure mathematics dynamical systems iteration of complex functions-Julia sets random fractals Brownian motion and Brownian surfaces multifractal measures physical applications.

6,325 citations

Book
01 Jan 1988
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
Abstract: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section. A bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images.

4,361 citations


Network Information
Related Topics (5)
Nonlinear system
208.1K papers, 4M citations
84% related
Particle
96.5K papers, 1.9M citations
82% related
Differential equation
88K papers, 2M citations
82% related
Boundary value problem
145.3K papers, 2.7M citations
82% related
Artificial neural network
207K papers, 4.5M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
20231,168
20222,380
20211,074
20201,026
20191,057