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, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. 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.
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.
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, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. 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.
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.

Computability of Julia Sets
151
Computability of Julia Sets
151Paperback(Softcover reprint of hardcover 1st ed. 2009)
Product Details
ISBN-13: | 9783642088063 |
---|---|
Publisher: | Springer Berlin Heidelberg |
Publication date: | 11/23/2010 |
Series: | Algorithms and Computation in Mathematics , #23 |
Edition description: | Softcover reprint of hardcover 1st ed. 2009 |
Pages: | 151 |
Product dimensions: | 6.10(w) x 9.25(h) x 0.01(d) |