Fractal dimensions and geometries of caves.
- Permanent Link:
- Fractal dimensions and geometries of caves.
- Series Title:
- Mathematical Geology
- Curl, Rane L.
- Springer Nature
- Publication Date:
- Subjects / Keywords:
- Caves ( local )
Fractals ( local )
Self-Similarity ( local )
- serial ( sobekcm )
- Lengths of all caves in a region have been observed previously to be distributed hyperbolically, like self-similar geomorphic phenomena identified by Mandelbrot as exhibiting fractal geometry. Proper cave lengths exhibit a fractal dimension of about 1.4. These concepts are extended to other self-similar geometric properties of caves with the following consequences.
Lengths of a cave is defined as the sum of sizes of passage-filling, linksed modular elements larger than the cave-defining modulus. If total length of all caves in a region is a self-similar fractal, it has a fractal dimension between 2 and 3; and the total number of linksed modular elements in a region is a self-similar fractal of the same dimension. Cave volume in any modular element size range may be calculated from the distribution.
The expected conditional distribution of modular element sizes in a cave, given length and modulus, also is distributed hyperbolically. Data from Little Brush Creek Cave (Utah) agree and yield a fractal dimension of about 2.8 (like the Menger Sponge). The expected number of modular elements in a cave equals approximately the 0.9 power of length of the cave divided by modulus. This result yields an intriguing â€œparlor trick.â€ An algorithm for estimating modular element sizes from survey data provides a means for further analysis of cave surveys.
- Original Version:
- Mathematical Geology, Vol. 18, no. 8 (1986-11).
- Source Institution:
- University of South Florida Library
- Holding Location:
- University of South Florida
- Rights Management:
- This object is protected by copyright, and is made available here for research and educational purposes. Permission to reuse, publish, or reproduce the object beyond the bounds of Fair Use or other exemptions to copyright law must be obtained from the copyright holder.
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