Computability of Julia Sets

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<P>Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. </P><P>Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, <EM>it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable</EM>. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. </P><P>The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems. </P>