COMPUTER-GENERATED FRACTALS WITH MEDICAL APPLICATION IN TRABECULAR BONE STRUCTURE

Abstract

Fractal can be described as a self-similarity, irregular shape and scale independent object. The generation of each fractal is dependent on the algorithm used. The fractal is generated using a form of computer-generated process to create complex, repetitive, mathematically based geometric shapes. There are two main aims of this research, one of which is to develop a prototype known as Fractal Generation System (FGS) whereby each type of fractal is generated by practical implementations of the theories with some adaptation in the following algorithms: IFS Iteration, Formula Iteration and Generator Iteration. FGS also caters for the calculation of the fractal dimension (FD) parameter using Box Counting Method (BCM). This parameter enables the system to characterize the irregularity and self-similarity of fractal shapes. FGS generates four types of fractals, which are Julia set, Mandelbrot set, Sierpinski Triangle and Koch Snowflake based on the three iterations. The FD values computed and fractal patterns generated by FGS agree well with theoretical values and existing fractal shapes. The second main aim is in relation to the importance of fractal application in the real world whereby it focuses on analyzing trabecular bone structure. Bone has fractal characteristics. CT-scan images of trabecular bones of 27 males and 26 females ranging between 25 to 81 years were analyzed. The CT-scan images were digitized to convert it to binary images. The images were then processed to obtain the FD parameter. The differences of the values due to gender and age are discussed in this thesis. There is a decrement of the FD values when the age increases for both male and female. This is due to an age-associated reduction in number of fine trabecular network. Male FD is generally higher than female FD. The rate of decrease in FD with age for male and female depends on the puberty, pre-menopausal and post-menopausal stages.