Fractals in the Fundamental and Applied Sciences: Proceedings of the First IFIP Conference on Fractals in the Fundamental and Applied Sciences, Lisbon, Portugal, 6-8 June 1990

This volume contains the proceedings of the first IFIP conference on fractals. The mathematical concept of fractal was coined by B.B. Mandelbrot in the early seventies to characterize objects with self-similar structures at all levels. Now the field of fractals is being subject to intensive research and an extensive growth of applications in many sciences. This first IFIP conference, intended as a start of periodic conferences on fractals, enables a productive cross fertilization of ideas among specialists in fractals and in information processing. In addition to the volume's 44 colour illustrations, on page v is a rare view of fractals and the Portuguese architecture at the time of the navigators, produced by Master Lima de Freitas, a leading Portuguese artist and member of the conference organizing committee. The design illustrates the symbiosis of mathematics and human artifacts represented by the real world.

Table of Contents:
Some Mathematical Models for the Pattern Growth in the Ordered Systems (M.A. Antonets, I.A. Shereshevsky). The Statistical Clusters Dynamics in the Dendroid Transport Systems (V.A. Antonets, M.A. Antonets, I.A. Shereshevsky). Characteristics of Anomalous Dynamic Diffusion (I.S. Aranson, M.I. Rabinovich, L.S. Tsimring). Selfsimilarity Within Limits: Description with the Log-Logistic Function (H.R> Bittner, M. Sernetz). Modelling of Fractal Vessel Systems (H.R. Bittner). Recurrent Iterated Function Systems: Invariant Measures, A. Collage Theorem and Moment Relations (C. Cabrelli, U. Molter, E.R. Vrscay). Fractal Dimensions of the Fine Scale Structures of Turbulence (G.D. Catalano, J.A. Mathis, K.S. Chang). Increasing the Accuracy of Fractal Dimensions Computed from the Richardson-Mandelbrot-Plot (R. Creutzburg, E. Ivanov). Euler Maclauren Type Expansions for some Fractal Measures (S. Demko). Onedimensional Fractal Functions, Measures and Distributions (S. Dubuc, F. Nekka). Fractals and Multifractals for Electrons in Non-Periodic Solids (S.N. Evangelou). A Fractal Approach to Musical Composition (B. Fagarazzi). Generation of Fractal Curves by Generalizations of Lindenmayer's L-Systems (E.G. Giessmann). A Probabilistde Look at the Chaos Game (G.S. Goodman). On the Derivation of Fractal Functions (M. Guzman, M.A. Martin, M. Reyes). Rendering Methods for Iterated Function Systems(D. Hepting, P. Prusinkiewiscz, D. Saupe). Numerical Investigation of Stochastic Processes with Memory (R. Ketzmerick). A Calculas on some Self-Similar Sets (J. Kigami). Techniques for Solving Inverse Fractal Problems (G. Mantica). Homogeneous Fractals and their Application in Texture Analysis (U. Mussigmann). Visualizing the Dynamics of Particle-Field Interactions (M.M. Novak). Comparison of Different Microbial Growth Patterns Described by Fractal Geometry (M. Obert, M. Sernetz, U. Neuschulz). Digital Sum Problems (A.H. Osbaldestin). Fractal Boundaries, Analyticity, and Generating Mechanism (J. Parisi, et al.). On a Fractal Julia Set Arising from the Toda Lattice (P. Petek). Synthesis of Space Filling Curves on the Square Grid (P. Prusinkiewicz, A. Lindenmayer, F.D. Fracchia). The Fractional Geometry of an Active Fault (A. Ribeiro, et al.). Simulation of Fractional Brownian Motion (W. Rumelin). Reactions on Fractals: The Case of Immobile Reactants (H. Shnorer, S. Luding, A. Blumen). A Garden of Fractals (H.F. Smith). Julia Sets with Polyhedral Symetries (S. Ushiki). Moment and Collage Methods for the Inverse Probem of Fractal Construction with Iterated Function Systems (E.R. Vrscay).