Book contents
- Frontmatter
- Contents
- Preface
- Preface to the second edition
- 1 Scale invariance
- 2 Definition of a fractal set
- 3 Fragmentation
- 4 Seismicity and tectonics
- 5 Ore grade and tonnage
- 6 Fractal clustering
- 7 Self-affine fractals
- 8 Geomorphology
- 9 Dynamical systems
- 10 Logistic map
- 11 Slider-block models
- 12 Lorenz equations
- 13 Is mantle convection chaotic?
- 14 Rikitake dynamo
- 15 Renormalization group method
- 16 Self-organized criticality
- 17 Where do we stand?
- References
- Appendix A Glossary of terms
- Appendix B Units and symbols
- Answers to selected problems
- Index
Appendix A - Glossary of terms
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Preface to the second edition
- 1 Scale invariance
- 2 Definition of a fractal set
- 3 Fragmentation
- 4 Seismicity and tectonics
- 5 Ore grade and tonnage
- 6 Fractal clustering
- 7 Self-affine fractals
- 8 Geomorphology
- 9 Dynamical systems
- 10 Logistic map
- 11 Slider-block models
- 12 Lorenz equations
- 13 Is mantle convection chaotic?
- 14 Rikitake dynamo
- 15 Renormalization group method
- 16 Self-organized criticality
- 17 Where do we stand?
- References
- Appendix A Glossary of terms
- Appendix B Units and symbols
- Answers to selected problems
- Index
Summary
ATTRACTOR A point in phase space toward which a time history evolves as transients die out.
BASIN OF ATTRACTION Some dynamical systems have more than one fixed point. The region in phase space in which solutions approach a particular fixed point is known as the basin of attraction of that fixed point. The boundaries of a basin of attraction are often fractal.
BIFURCATION A change in the dynamical behavior of a system when a parameter is varied.
BROWNIAN WALK The running sum of a sequence of random values usually obtained from a normal distribution.
CANTOR DUST A fractal set generated by subdividing a line into parts.
CHAOS Solutions to deterministic equations are chaotic if adjacent solutions diverge exponentially in phase space; this requires a positive Lyapunov exponent.
CLUSTER A group of particles with nearest-neighbor links to other particles in the cluster.
DETERMINISTIC A dynamical system whose equations and initial conditions are fully specified and are not stochastic or random.
DIFFERENCE EQUATION An equation that relates a value of a function xn+1 to a previous value xn. A difference equation generates a discrete set of values of the function x.
DIFFUSION-LIMITED AGGREGATION (DLA) Diffusing (random-walking) particles accrete to a seed particle to form a dendritic structure.
DIMENSION The usual definition of dimension is the topological dimension. The dimension of a point is zero, of a line is one, of a square is two, of a cube is three. In this book we have introduced the concept of fractional (noninteger) dimensions, or fractals.
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- Information
- Fractals and Chaos in Geology and Geophysics , pp. 371 - 373Publisher: Cambridge University PressPrint publication year: 1997