TY - BOOK ID - 7543123 TI - Computability of Julia Sets AU - Braverman, Mark. AU - Yampolsky, Michael. PY - 2009 SN - 3642088066 3540685464 9786612006395 1282006398 3540685472 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Algebra. KW - Algorithms. KW - Computer science. KW - Computer software. KW - Information theory. KW - Julia sets. KW - Julia sets KW - Engineering & Applied Sciences KW - Mathematics KW - Physical Sciences & Mathematics KW - Geometry KW - Computer Science KW - Data processing KW - Fractals. KW - Data processing. KW - Fractal geometry KW - Fractal sets KW - Geometry, Fractal KW - Sets, Fractal KW - Sets of fractional dimension KW - Sets, Julia KW - Mathematics. KW - Computer programming. KW - Computers. KW - Computer science KW - Programming Techniques. KW - Theory of Computation. KW - Algorithm Analysis and Problem Complexity. KW - Mathematics of Computing. KW - Dimension theory (Topology) KW - Fractals KW - Software, Computer KW - Computer systems KW - Communication theory KW - Communication KW - Cybernetics KW - Informatics KW - Science KW - Mathematical analysis KW - Algorism KW - Algebra KW - Arithmetic KW - Foundations KW - Computer science—Mathematics. KW - Automatic computers KW - Automatic data processors KW - Computer hardware KW - Computing machines (Computers) KW - Electronic brains KW - Electronic calculating-machines KW - Electronic computers KW - Hardware, Computer KW - Machine theory KW - Calculators KW - Cyberspace KW - Computers KW - Electronic computer programming KW - Electronic data processing KW - Electronic digital computers KW - Programming (Electronic computers) KW - Coding theory KW - Programming UR - https://www.unicat.be/uniCat?func=search&query=sysid:7543123 AB - 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. 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 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. ER -