The Escape Buffer : Efficient Computation of Escape Time for Linear Fractals

Daryl H. Hepting School of Computing Science Simon Fraser University Burnaby, British Columbia CANADA V5A IS6 e-mail: darylh@cs .sfu .ca The study of linear fractals has gained a great deal from the study of quadratic fractals , despit e important differences. Methods for classifying points in the complement of a fractal shape were originally dev elop ed for quadratic fractals , to provid e insight into their und erlying dynami cs. These methods were later inodified for use with linear fractals . This paper reconsiders one such classification , called escape tim e, and presents a new algorithm for its computation that is significantly fas t er and conceptually simpler. Previous methods worked backwards, by mappin g pixels into classifi ed reg ions , wh e reas th e ne w forward algorithm uses an "esca p e buffer" to mapping classified regions onto pixels. The effi ciency of the escape buffe r is justifi ed by a careful analysis of its pe rforman ce on lin ea r fractals with various prop erti es .