Amir, Shahizat (2013) Modeling and simulation of single and multiple cluster fractals cultured in polymer films / Shahizat bin Amir. PhD thesis, University of Malaya.
Abstract
Study of fractals has been an interest for scientists and mathematicians since the term ‘fractal’ was first coined by Mandelbrot. By a simple definition, a fractal is a shape made of parts similar to the whole in some way. Many studies on fractals have been carried out either in applications, usually involving experimental works, or in theory, where most simulations on fractal patterns models are on nature-based fractals such as river flows, coastline and tree branching. Many of fractal growth models are suitable with experimental phenomena such as electrochemical electrodeposition, electrochemical polymerization and Diffusion Limited Aggregation growth structures of many metal aggregates in the presence of a magnetic field as external stimuli. The formation of fractals without using any external stimuli has been reported by a few groups of researchers. This work focuses on the improvisation of the modeling and simulation of laboratory cultured fractals using polymer electrolyte films as the media of growth. This research work’s main topics are fractals and fractal growth models particularly DLA (Diffusion Limited Aggregation). DLA model describes how a fractal is built from particles in low concentrations. The DLA cluster formed through DLA is formed by particles moving due to Brownian motion (diffusion) which meet and stick together randomly (aggregation) to form the cluster. Fractals can be constructed using this model from polymer films infused with inorganic salt without any external stimuli. The experimental methods for growing fractals are discussed. This research work also includes descriptions of polymer films properties and the advantages of using polymer films infused with inorganic salt as media to culture fractals. The simulation of single and multiple cluster fractals is done using DLA methods incorporating different parameters such as its sticking coefficient, lattice geometry and number of particles. Development of a computer coding to simulate and visualize the fractal growth is a key part in this research. To compare the simulation with the real patterns obtained, one vital aspect would be the calculation of their fractal dimension values. The computer program developed is able to calculate the fractal dimension value of each of the simulated fractal patterns. Suitable fractal dimension calculation method is employed according to its usefulness and efficiency. Fractal growth modeling and simulation such as done here can contribute to the understanding of other related studies concerning fractal growth found in areas including medical (nervous systems, cancer growth and more).
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