Quantitative Analysis of Organism Growth Using Fractal Dimension Statistics

Philippine Science High School
Maria Moper Dionaleigh B. Nune


Cultures of bacteria were analyzed using fractal geometry and statistics to provide a method for predicting organism growth, paving the way for a better design of treatment drugs. Images of three cultures of isolated Bacillus subtilis were taken at time intervals of two to three hours for eight days. The images were processed using the IDOLON program and quantitatively described using three statistical formulas: fractal dimension D, Renyi dimension and Hausdorff-Besicovitch dimension. The three variables were integrated to compute the maximum of the distribution and were used as coordinates for a 3-dimensional graph f. A 2-dimensional graph g containing the maximum of a distribution under time analysis was also constructed. Topological properties of the graphs, including slope, direction and area were used to determine the interrelationship of the three fractal values. The two graphs, described as φ - : X -? P1 where X is the smooth algebraic assimilation of the four variables under time analysis, was extended using Java. A computer-aided prediction model of the graphs f and g were made which combined the topology of f and g at infinity. The computed fractal values showed the existence of a fractal pattern in the growth of Bacillus subtilis with fractal dimension ranging from 0.900 to 4.000, indicating a linear iteration. This was supported by the values of the Renyi dimension, which showed a horizontal growth pattern of the bacterial cultures, establishing the growth of the bacteria to be inclined to go towards the North East direction. There was consistency in the computed fractal values, maximum of distribution and topographical computations of all three cultures which also indicated the existence of a pattern of growth which could be extended to tinfinity, thereby allowing prediction of the direction and rate of growth of the bacterial colonies. The fractal patterns in the growth of bacteria, in this case Bacillus subtilis, yielded the direction and rate of growth of the bacteria as shown by the analysis of the fractal patterns and statistical values, showing that the growth of harmful organisms can therefore be predicted, making it possible to improve on the design of drugs for the control of perilous cells. By preventing the growth of insidious cells, the potential effects of virulent organisms may be avoided, and treatment may be made more possible.

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