Self-Similarity Pattern Corresponding to the Vegetational Field Data

Background/Objectives: A study was conducted to observe the self-similarity pattern exhibited within the vegetational field due to their nutritional sharing channels. Methods/Statistical Analysis: A square grid matrix was chosen in the cultivated fields to draw the sample data of the biological as well as environmental variables. Grid matrix was further divided into one hundred and forty -four subareas of 1.2 by 1.2-meter square. Data were analyzed based on a Box-counting method to determine the fractal dimension in each class. Findings: Highest dimension was found to be 2.48 in class one which consists of 144 small grids. Whereas, the lowest dimension found to be 1.03 in class 4. The pattern of the fractal dimension of various classes seems to be self-similar within the vegetational field. Application/Improvements: Vegetational fields share several materials through the nutritional channels within the grid matrix. We observed the pattern in different scales using fractal dimension and found to be the self-similar pattern in all scales. *Author for correspondence


Introduction
Fractal analysis is very worthwhile for the ecologist for describing the ecological processes. Detecting and describing the pattern in the distribution of vegetation can be instrumental in understanding the factors which influence how and where plants grow, and the role played by plants in shaping ecosystems. In 1 general, the pattern can either be due to internal characteristics of the plants or to external environmental factors the occurrence of individual plants can be limited by vegetative propagation, seed dispersal or micro-environmental factors 2 .
Detecting patterns through space or time considered a central goal of landscape ecology and to conclude those patterns through multiple scales 3-4 . Self-similarity is the characteristics of Fractal used to distinguish achieving the research goals 5 . These approaches are very fruitful to the field of landscape ecology and address explicitly to measures the symmetry at various scales. Moreover, investigators generalize the process at a wide range of scales to entertain questions concerning the patterns process to look at the appropriate scales 6 . The fractal analysis allows ecologists to map growth pattern of plants and influencing nematode and bacteria without creating an unmanageable deluge of information. Natural fractals can be either statistically self-scaling (the patterns at different scales are qualitatively different but have the same fractal Keywords: Box-Counting Method, Fractal Dimension, Self-Similar Pattern dimension 'D'), or this dimension 'D' can change at different scales of measurement.

Materials and Methods
The proposed study was conducted within the fertile field cultivated generally seasonal crop (tomato and guar) grown in rotation. A 12 by 12-meter square grid matrix was chosen and further divided into one hundred and forty-four small quadrats of 1.2 by 1.2-meter square each. Grid matrix was further divided into four classes so that to study the self -similar pattern at various scale. Study area consist 432 samples of tomato plants in which nematode soil population and its associated three soilborne fungi (Fusarium solani, Paecilomyces lilacinus and Aspergillus spp.), were recorded in the data matrix. Population distribution of nematode and associated soil fungi showed quietly sparse throughout the field plot of 144 grids. Almost all fields consist non-zero values of nematode and fungi.
The box-counting method was used to determine the fractal dimension of each class. Several fungi were obtained during the study, but the analysis was performed only for the nematodes soil population. The fractal dimension of the species variables such as plant parasitic nematode and its associated soil fungi (Fusarium Solani, Paecilomyces lilacinus, and Aspergillus spp.), and environmental variables such as soil moisture percentage, organic matter contents, pH, CaCO 3 , NO 3 , P, K were analyzed.
Fractal is a shape made of parts similar to the whole in some way 7,8 . Whereas, box counting is a method which collect the information from the fields into data grid matrices and analyzed the complex patterns by dividing the data matrix into further smaller and smaller scale of block sizes to measure the patterns in larger to small scales. However, the prime essence of this technique is to observe the patterns in very small scale. The fractal dimension 'D' , uses the power law technique and it is the quotient of two logarithms (Eq-1,2): N = a D [1] log N = log a D log N = D log a D = log N [2] log a

Results and Discussion
The fractal dimension of each class was calculated. Highest dimension was found to be 2.48 in class one which con-  sists 144 small grids and lowest dimension as 1.03 was found in class 4. Whereas, 2.63 and 1.16 dimensions from high to low were found to be within the nematode soil population. The pattern of the fractal dimension of various classes seems to be self-similar within the vegetation field (Figures -1a,1b,1c,1d).

Conclusion
Our study revealed that the pattern formation of the fractal dimension of the nematode soil population within the vegetational field of various grid sizes produced self-similar pattern regardless of the size of the grid matrix.

Acknowledgement
This study is funded by the Higher Education Commission of Pakistan through its NRPU grant project No. 6245.