Introduction to Fractals

Abstract

Throughout the ages man has marveled at nature. The dimension of observation has increased from the eye to the electron microscope. All natural phenomena as observed by man seem very complex, at least at first sight. It may be the shape of riverbanks or hills or waves at the beach. Or it can be the shapes and colors of butterflies, leaves, and flowers, or the skin patterns (on the leopard or zebra). We may include here the shape of coastlines or of snowflakes. And we may also include the stars in the sky, the galaxy, and our solar system. The size range that has been studied varies from the shapes of craters on the moon, to the microscopic-level analyses of porous solid surfaces (catalysts, geological formations, oil reservoirs). Man is inquisitive, and therefore questions why he is here on earth, and whether the various phenomena mentioned above can be described by some mathematical geometry. Furthermore, man studies evolution and the ecological processes, which are in some ways related to these shapes and forms.