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...Introduction in the past mathematics has been concerned largely with sets and functions to which methods of classical calculus can be applied or that are not sufciently smooth regular have tended ignored as pathological worthy study certainly they were regarded individual curiosities only rarely thought a class general theory might applicable recent years this attitude changed it realized great deal said is worth saying about non objects moreover irregular provide much better representation many natural phenomena than do gures geometry fractal provides ageneralframeworkforthestudyofsuchirregularsets we begin by looking briey at number simple examples fractals note some their features middle third cantor set one best known most easily con structed nevertheless displays typical characteristics constructed from unit interval sequence deletion operations see gure let e recall denotesthesetofreal numbers x such b obtained deleting mid dle sothate consists two intervals thirds these gives th...