Knowledge Mining In Fractal Geometry Patterns

Abstract

Nature abounds with the periodic phenomena; from the motion of as wing to the oscillations of atoms, from sunrise to the sunset. But in nature there are numerous other phenomena in which linearity breaks down and instead of periodicity, we get aperiodic or chaotic motion. For example, the smooth waves on a well behaved lake turn to violent turbulence in the mountain brook, and the daily sunrise is overshadowed by cloud formation. newlineFractals have shown the ability to describe the natural phenomena. A fractal is a nonlinear geometric object which is rough or irregular on all scales of length, so it appears to be broken up in a radical way. Fractals are said to possess infinite details. In many cases, a fractal can be generated by a repeating pattern, in a typically recursive or iterative process. Objects that are now called fractals were discovered and explored long before when the word was coined in 1975 by B. B. Mandelbrot. newlineVerhulst logistic map f(x) = r x (1 - x) is a widely studied and applicable model in discrete dynamical system. The discrete time variable version of Verhulst s growth law, the logistic map, is the foundation stone for the theory of nonlinear dynamics, and basis of modern chaos theory. In English language chaos means state of total disorder or mismanagement. Although there is no universal definition of chaos, this is the general acceptance that the breakdown of predictability is called chaos. The term chaos was proposed by Yorke and Li. newlineKnowledge mining is effective in the sense that it can discover new knowledge not only from the large amount of data but also from the limited and weakly relevant data. Knowledge mining uses multi-strategy methodology to derive high level concepts and descriptions. It deals with the symbolic reasoning process on the data available and relevant background knowledge of the context. For knowledge extraction and effective decision making from variety of data, some powerful methods are used. Pattern recognition, clustering techniques, machine learning, statistical dat