The Escape Time Dimension of the Filled Julia Set

Abstract

Our objective in this paper is to invent a new method for counting the dimension of fractals constructed by the Escape Time Algorithm using the method of spreading the points inside the proposed window and we call this dimension the Escape Time dimension of the Escape Time fractals. We find the Escape Time dimension of the filled Julia set Fc (which has not be evaluated before) associated with the function fc: C C defined by: fc (z)  z2 + c, where c  C. And we also find the Escape Time dimension of filled Julia set( ) associated with , for each iteration n. And we find that DE(Fc(fc))  .