Fractal dimensions and geometries of caves.

Citation

Material Information

Title:
Fractal dimensions and geometries of caves.
Series Title:
Mathematical Geology
Creator:
Curl, Rane L.
Publisher:
Springer Nature
Publication Date:
Language:
English

Subjects

Subjects / Keywords:
Caves ( local )
Fractals ( local )
Self-Similarity ( local )
Genre:
serial ( sobekcm )

Notes

Abstract:
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 “parlor trick.” 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).

Record Information

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.

USFLDC Membership

Aggregations:
University of South Florida
Karst Information Portal

Postcard Information

Format:
serial

printinsert_linkshareget_appmore_horiz

Download Options

close

No images or PDF downloads are available for this resource.


Cite this item close

APA

Cras ut cursus ante, a fringilla nunc. Mauris lorem nunc, cursus sit amet enim ac, vehicula vestibulum mi. Mauris viverra nisl vel enim faucibus porta. Praesent sit amet ornare diam, non finibus nulla.

MLA

Cras efficitur magna et sapien varius, luctus ullamcorper dolor convallis. Orci varius natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Fusce sit amet justo ut erat laoreet congue sed a ante.

CHICAGO

Phasellus ornare in augue eu imperdiet. Donec malesuada sapien ante, at vehicula orci tempor molestie. Proin vitae urna elit. Pellentesque vitae nisi et diam euismod malesuada aliquet non erat.

WIKIPEDIA

Nunc fringilla dolor ut dictum placerat. Proin ac neque rutrum, consectetur ligula id, laoreet ligula. Nulla lorem massa, consectetur vitae consequat in, lobortis at dolor. Nunc sed leo odio.