Fractals everywhere
Theoretical Computer Science
The computational complexity of some julia sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Jordan Curves with Polynomial Inverse Moduli of Continuity
Electronic Notes in Theoretical Computer Science (ENTCS)
Constructing non-computable Julia sets
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Jordan curves with polynomial inverse moduli of continuity
Theoretical Computer Science
On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane
Electronic Notes in Theoretical Computer Science (ENTCS)
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Electronic Notes in Theoretical Computer Science (ENTCS)
On the complexity of computing the logarithm and square root functions on a complex domain
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
How can nature help us compute?
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
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Although numerous computer programs have been written to compute sets of points which claim to approximate Julia sets, no reliable high precision pictures of non-trivial Julia sets are currently known. Usually, no error estimates are added and even those algorithms which work reliable in theory, become unreliable in practice due to rounding errors and the use of fixed length floating point numbers. In this paper we prove the existence of polynomial time algorithms to approximate the Julia sets of given hyperbolic rational functions. We will give a strict computable error estimation w.r.t. the Hausdorff metric on the complex sphere. This extends a result on polynomials z@?z^2+c, where |c|