A Starting Point for the Randomwalk; What Use are Fractals?; Delinquent Coins and Staggering Drunks; Fractal Systems Generated by Randomwalks in Two-Dimensional Space; Vanishing Carpets, Fractal Felts and Dendritic Capture Trees; An Exploration of the Physical Significance of Fractal Structures in Three-Dimensional Space; Fractal Fingers and Floods; Fracture, Fragments and Fractals; Signposts to More Rambling Explorations of Fractal Space.