Front cover image for Curves and fractal dimension

Curves and fractal dimension

Written for mathematicians, engineers, and researchers in experimental science, as well as anyone interested in fractals, this book explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length.
Print Book, English, ©1995
Springer-Verlag, New York, ©1995
xiv, 323 pages : illustrations ; 24 cm
9780387940953, 9783540940951, 0387940952, 3540940952
28183123
Foreword / Michel Mendes France
pt. I. Sets of Null Measure on the Line. 1. Perfect Sets and Their Measure. 2. Covers and Dimension. 3. Contiguous Intervals and Dimension
pt. II. Rectifiable Curves. 4. What Is a Curve? 5. Polygonal Curves and Length. 6. Parameterized Curves, Support of a Measure. 7. Local Geometry of Rectifiable Curves. 8. Length, by Intersections with Straight Lines. 9. The Length by the Area of Centered Balls
pt. III. Nonrectifiable Curves. 10. Curves of Infinite Length. 11. Fractal Curves. 12. Graphs of Nondifferentiable Functions. 13. Curves Constructed by Similarities. 14. Deviation, and Expansive Curves. 15. The Constant-Deviation Variable-Step Algorithm. 16. Scanning a Curve with Straight Lines. 17. Lateral Dimension of a Curve. 18. Dimensional Homogeneity
pt. IV. Annexes, References and Index. A. Upper Limit and Lower Limit. B. Two Covering Lemmas. C. Convex Sets in the Plane