The Escape Buuer: Eecient Computation of Escape Time for Linear Fractals

The study of linear fractals has gained a great deal from the study of quadratic fractals, despite important dierences. Methods for classifying points in the complement of a fractal shape were originally developed for quadratic fractals, to provide insight into their underlying dynamics. These methods were later modied for use with linear fractals. This paper reconsiders one such classication, called escape time, and presents a new algorithm for its computation that is signicantly faster and conceptually simpler. Previous methods worked backwards, by mapping pixels into classied regions, whereas the new forward algorithm uses an \escape buer" to mapping classied regions onto pixels. The eeciency of the escape buer is justied by a careful analysis of its performance on linear fractals with various properties.