Fractal and shape analyses of manganese dendrites on vein quartz

Author : T. F. Ng & G.H. Teh
Publication : Bulletin of the Geological Society of Malaysia
Page : 73-79
Volume Number : 55
Year : 2009

Bulletin of the Geological Society of Malaysia, Volume 55, November 2009, pp. 73-79


Fractal and shape analyses of manganese dendrites on vein quartz

T. F. Ng* & G.H. Teh

Department of Geology, University of Malaya, 50603 Kuala Lumpur, Malaysia

*Email address:


Abstract— Manganese dendrites are common along joint planes in a quartz vein in Selayang, northern Kuala Lumpur. Individual dendrites mainly range from about 5 cm to 50 cm in length. They have variable shapes that range from simple shape with few branches to complex intricately branched patterns. Dendrites having different patterns may be found together along the same joint plane and some simple dendrites developed into more intricate forms. Digital photographs of dendrites were taken in the field and then converted to single bit images for fractal analysis. The images were also vectorised to measure the perimeter and area of the dendrites as well as the enclosing convex hull. These basic measurements were used to obtain the fractal dimension, lacunarity, PARIS factor, divergent ratio, fractal divergent ratio and fill factor for nine samples, which cover dendrites of various forms and complexities.

The fractal dimension of the dendrites measured using box counting algorithm ranges from 1.57 to 1.88. Generally, dendrites with broad and short branches have larger fractal dimension and those that have thin and long branches have smaller fractal dimension. Lacunarity and fill factor also show the same trend, while PARIS factor, divergent ratio and fractal divergent ratio values are higher in complex and intricately branched dendrites. There are dendrites with similar fractal dimension but have dissimilar patterns. At the same fractal dimension, the lacunarity is smaller for more complex and intricately branched dendrites, while the fractal divergent ratio is larger for dendrites with thinner branches. Although the values of both PARIS factor and divergent ratio increase with the increase in the intensity of branching, these parameters cannot be clearly related to the variation in the pattern of dendrites.


Keywords: Manganese dendrites, fractal dimension, lacunarity, shape factors