The Fractal Factor: Fractals in Condensed Matter Physics, Fractal Analysis of Random Walk with Memory, Fractal Structures in Kinetic Critical Phenomenon

BB Mandelbrodt was the first to realize that the familiar shapes in nature --- from coastline to lightning , possess the property of self similarity and can be described by means of a new kind of of geometrical shape that he named' fractals' from the Latin 'fractus' meaning fragmented. The concept was definitely lacking for the description of complex structures in nature; these objects, we all know, are in the vast majority. This fact alone explains the reason for the huge success of fractal studies-- from its application to condensed matter physics to investigating financial markets. A deepening of the inter relation between fractal geometry and the physical phenomena is what may be termed as the theory of fractals, and forms the primal objective of the present activity in the field. There are two streams of activities with regard to the impact of fractal studies. The first one tries to answer the question:' where do fractals come from?'. The other view point is that the fractal structures do exist :' what are their physical properties?'. EWE have attempted to incorporate both view points in this manuscript.