Mark Braverman is deeply engaged in fostering understanding and peace through his work with the Holy Land Education and Peace building Project. This grassroots initiative champions interfaith dialogue, conflict resolution, and peace-building efforts in the Middle East. Braverman's dedication lies in building bridges between different communities and promoting a more harmonious coexistence. His commitment to these vital causes shapes his unique perspective.
Mark Braverman reveals the true nature and shocking consequences of the conflict between Israel and Palestine, explaining why Zionism is not a true Christian response to the conflict and offering clear-cut solutions for peace at home and abroad.
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 (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.