Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Computability of Julia Sets

Computability of Julia Sets

Braverman, Mark
Yampolsky, Michael

Paperback

Series: Algorithms and Computation in Mathematics, Book 23

AlgebraGeneral ComputersGeneral Mathematics

ISBN10: 3642088066
ISBN13: 9783642088063
Publisher: Springer
Published: Nov 22 2010
Pages: 151
Weight: 0.54
Height: 0.36 Width: 6.14 Depth: 9.21
Language: English

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.

Also from

Braverman, Mark

View All

Also in

General Mathematics

View All