Estudio fractal de la superficie de la hoja de la especie vegetal Copaifera sp. haciendo uso del Microscopio de Fuerza Atómica-AFM

Abstract

The species of Copaifera sp. which are also called copal are widely used in folk medicine due to its ethnopharmacological properties. This work was accomplished with the purpose of the possibility of standardization of the leaves, on the study of the surface texture of the leaf, for this you need to obtain the fractal parameters as fractal dimension (roughness, porosity), lacunarity (rotational invariance of the holes ) and succolarity (percolation), making use of the data of the Atomic Force Microscopy (AFM) worked with the optimal area (25x25 mm²), with the data process and applying fractal mathematics, algorithms were developed with the computer program Fortran 77. The study was conducted from difficulty that one has to distinguish one species from another of Copaifera sp., and to make such identification is needed flower and leaf Copaifera sp., this is because the plant blooms only once a year. That's why it is proposing an easier and effective way to such identification, only making use of leaf Copaifera sp. for the calculation of the fractal dimension. It will make use of Box Counting method for its simplicity and exactitude, which will serve to calculate the roughness and porosity of the surface of the sheet Copaifera sp. It is expected that the value of roughness obtained by the Fractal geometry is more accurate, the calculation of roughness with Euclidean mathematics. The Lacunarity is another fractal parameter used to determine readily the uniformity of the holes for the calculation of lacunarity be made using the method of the counting boxes (Differential Box Counting) which is a method based on the counting boxes (Box-Counting), but the lacunarity is much greater than one, there is greater disorder of the holes.The lacunarity is closer to 1, there is less clutter, now the lacunarity is equal to 1, the surface is completely uniform, is down is invariant rotation, it is expected that lacunarity of Copaifera sp leaf is close to an a succolarity is the last fractal parameter that is doing applied to the study of surfaces, which measures the ability of a flow through the entire surface that serves to measure the percolation surface level. It is measured succolarity in the four directions is down from above down, bottom-up, from left to right, and finally from right to left. When it has calculated the three fractal parameters: fractal dimension, lacunarity and succolarity, it is possible to have fully characterized the leaf surface.