Generation of 3D Fractal Images for Mandelbrot and Julia Sets

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in domains ranging from multi-coloured, multi-patterned fractal landscapes of natural geographic entities, image compression to even modelling of molecular ecosystems. Fractal geometry provides a basis for modelling the infinite detail found in nature. Fractals contain their scale down, rotate and skew replicas embedded in them. Many different types of fractals have come into limelight since their origin. This paper explains the generation of two famous types of fractals, namely the Mandelbrot Set and Julia Set, the3D rendering of which gives a real-world look and feel in the world of fractal images

Bounding the Attractor of an IFS

Fractal images defined by an iterated function system (IFS) are specified by a finite number of contractive affine transformations. In order to plot the attractor of an IFS on the screen of a digital computer, it is necessary to determine a bounding area for the attractor. Given a point on the plane, we obtain a formula for the radius of a circle centred on that point that contains the attractor of the IFS. We then describe an algorithm to find the point on the plane such that the bounding circle centred on that point has minimum radius

Computer generation and rendering of terrain

Computer Generation and Rendering of Terrain explores different techniques that are currently used in computer science to generate terrain data. Also explored are some techniques for rendering the terrain on a computer display. A new three step technique for the generation of terrain that is based on geometric characteristics is presented, as is a hybrid rendering technique

Parallel Graph Grammars with Instantiation Rules Allow Efficient Structural Factorization of Virtual Vegetation

Parallel rewriting of typed attributed graphs, based on the single-pushout approach extended by connection transformations, serves as the backbone of the multi-paradigm language XL, which is widely used in functional-structural plant modelling. XL allows to define instantiation rules, which enable an instancing of graphs at runtime for frequently occurring substructures, e.g., in 3-d models of botanical trees. This helps to save computer memory during complex simulations of vegetation structure. Instantiation rules can be called recursively and with references to graph nodes, thus providing a unifying formal framework for various concepts from the literature: object instancing, structural factorization, Xfrog multiplier nodes, L-systems with interpretation. We give simple examples and measure the computation time for an idealized growing virtual plant, taken from the GreenLab model, in its implementation with instantiation rules in XL, compared to a version without instantiation rules