author : Armin Bunde

A collection of chapters on some recent applications of fractals, mainly to biology and chemistry.

(Includes a Mac disk of demo software.)

Contents

• Armin Bunde, Shlomo Havlin.

A Brief Introduction to Fractal Geometry

A whistle-stop tour of fractal dimension, the Koch snowflake, Sierpinski gasket, Cantor dust, Julia sets, random walks, diffusion limited aggregation, and percolation

• Per Bak, Michael Creutz.

Fractals and Self-Organized Criticality

An overview of self-organised criticality, and how it is that systems can move themselves into this state. A lot about sand piles.

• Sergey V. Buldyrev, Ary L. Goldberger, Shlomo Havlin, C.-K. Peng, H. Eugene Stanley.

Fractals in Biology and Medicine: from DNA to the heartbeat

Recent progress applying fractal concepts to biology and medicine: lung airways, arterial system, cauliflower heads, neuron shape, viscous fingering, bacterial colony spread, information coding in DNA, heartbeats, evolutionary extinctions

• János Kertesz, Tamas Vicsek.

Self-Affine Interfaces

Self-affine systems (self-similar, but with different scale factors along different directions): roughness of surfaces, growth of surfaces

• George H. Weiss.

A Primer of Random Walkology

Brownian motion, diffusion. Random walks on a lattice, continuous-time random walk, random walks in disordered media.

• Mohamed Daoud.

Polymers

Linear chains, self avoiding random walks, adsoption

• Sidney Redner, Francois Leyvraz.

Kinetics and Spatial Organization of Competitive Reactions

Two species A and B reacting, A+B-->I, where I is inert

• David Avnir, Ricardo Gutfraind, Dina Farin.

Fractal Analysis in Heterogeneous Chemistry

The structure and geometry of the reaction environment

• Dennis C. Rapaport, Martin Meyer.

Computer Exploration of Fractals, Chaos, and Cooperativity

An overview of the accompanying software