Fractals are universal in nature,found both in the arts[1] and in the scientific study of diverse fields,such as coastlines,[2] earthquakes,[3] and DNA knots.[4] Although fractals are ubiquitous,and relevant geometric issues about recursive self-similarity were studied as early as the 17th century by mathematician Gottfried Leibniz according to Pickover,[5] researchers have not been well motivated to explore this phenomenon.Thus these unfamiliar emerging concepts have remained obscured to mathematicians for centuries.However,Mandelbrots coining of the word fractal to describe a class of pattes possessing selfsimilarity which produces fine structure,and his use of fractals to explain a coastlines infinite length has drawn attention back to this familiar but not well-investigated field.Fractal research is now developing practical applications in geology,medicine neuroscience,and so on.Many computer-based methods are now available to generate and estimate fractal pattes,so one can visualize the beauty and appreciate some of the implications of the pattes discovered.