Data Mining Practical Machine Learning Tools and Techniques

Measuring the Strangeness of Strange Attractors

Acts in what Hutchinson (1965) has called the 'ecological theatre' are played out on various scales of space and time. To understand the drama, we must view it on the appropriate scale. Plant ecologists long ago recognized the importance of sampling scale in their descriptions of the dispersion or distribution of species (e.g. Greig-Smith, 1952). However, many ecologists have behaved as if patterns and the processes that produce them are insensitive to differences in scale and have designed their studies with little explicit attention to scale. Kareiva & Andersen (1988) surveyed nearly 100 field experiments in community ecology and found that half were conducted on plots no larger than 1 m in diameter, despite considerable differences in the sizes and types of organisms studied. Investigators addressing the same questions have often conducted their studies on quite different scales. Not surprisingly, their findings have not always matched, and arguments have ensued. The disagreements among conservation biologists over the optimal design of nature reserves (see Simberloff, 1988) are at least partly due to a failure to appreciate scaling differences among organisms. Controversies about the role of competition in structuring animal communities (Schoener, 1982; Wiens, 1983, 1989) or about the degree of coevolution in communities (Connell, 1980; Roughgarden, 1983) may reflect the

https://www.jstor.org/stable/info/2389612

Spatial Scaling in Ecology

Thirty-seven programs that summarize data with histograms and other graphics, calculate measures of spatial continuity, provide smooth least-squares-type maps, and perform stochastic spatial simulation.

GSLIB: Geostatistical Software Library and User's Guide

https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(06)68880-6.pdf

Mild cognitive impairment

Causality Principle, Deterministic Laws and Chaos.- The Backbone of Fractals: Feedback and the Iterator.- Classical Fractals and Self-Similarity.- Lim and Self-Similarity.- Length, Area and Dimension: Measuring Complexity and Scaling Properties.- Encoding Images by Simple Transformations.- The Chaos Game: How Randomness Creates Deterministic Shapes.- Recursive Structures: Growing Fractals and Plants.- Pascal's Triangle: Cellular Automata and Attractors.- Irregular Shapes: Randomness in Fractal Constructions.- Deterministic Chaos: Sensitivity, Mixing, and Periodic Points.- Order and Chaos: Period-Doubling and Its Chaotic Mirror.- Strange Attractors: The Locus of Chaos.- Julia Sets: Fractal Basin Boundaries.- The Mandelbrot Set: Ordering the Julia Sets.

Chaos and Fractals: New Frontiers of Science

Chaos and Fractals

Contents: Foreword: People and Events Behind the "Science of Fractal Images".- Fractals in Nature: From Characterization to Simulation.- Algorithms for Random Fractals.- Color Plates and Captions.- Fractal Patterns Arising in Chaotic Dynamical Systems.- Fantastic Deterministic Fractals.- Fractal Modelling of Real World Images.- Fractal Landscapes Without Creases and with Rivers.- An Eye for Fractals.- A Unified Approach to Fractal Curves and Plants.- Exploring the Mandelbrot Set.- Bibliography.- Index.

The science of fractal images

A can made of a steel sheet the surface of which is coated with a three-layered chromium coating, consisting of a metallic chromium coating, a crystalline chromium oxide coating and a non-crystalline hydrated chromium oxide coating in this order. A layer of an organic enamel or fused film may be provided further on top of the non-crystalline hydrated chromium oxide coating.

Heinz-Otto Peitgen

Papers

Chaos and Fractals: New Frontiers of Science

Chaos and Fractals

The science of fractal images

The Beauty of Fractals

Functional Differential Equations and Approximation of Fixed Points