We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c > 0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on the value of the Hausdorff dimension dH obtained from scaling properties of two point functions defined in terms of geodesic distance. Further insight to t...

a r t i c l e i n f o a b s t r a c t This paper describes a digital watermarking scheme based on fractal codification for 8-bit gray scale images; it replaces range blocks by modified blocks according to the watermark bit being embedded. The main contribution of this work is a decrease in the distortion generated by the watermark embedding in the carrier image compared to the reference scheme ...

So far, several implementations of the Fractal specifications have been proposed. These implementations propose frameworks for programming with Fractal in a target language (Java, C, Smalltalk, C++). The general principles of implementing the specifications are common to all these frameworks. However, as far as we know, no concrete piece of software or no common set of internal interfaces have ...

The paper presents a novel interactive application created in the C# programming language under the Microsoft Visual Studio environment: its introduction, theoretical grounds and application. The application allows generating two-dimensional fractals defined by iterated function systems and performing their arbitrary affine transformation. Most importantly, this transformations are easily contr...

Recent numerical results on the fractal structure of two-dimensional quantum gravity coupled to c = −2 matter are reviewed. Analytic derivation of the fractal dimensions based on the Liouville theory and diffusion equation is also discussed. Excellent agreements between the numerical and theoretical results are obtained. Some problems on the non-universal nature of the fractal structure in the ...