A Novel Web Application for Modeling 3 D Fractals

This paper introduces a novel application for generating and interactively modeling three-dimensional fractals defined by iterated function system (IFS). The modeling is achieved by means of control points, just like Bezier curves and surfaces are controlled. Unlikely the common way for transforming 3D fractals used in some existing software applications, by setting parameters of the required affine transformations and regenerating fractals, in this application the modeling is free and visually intuitive. There are two ways of defining control points (which are vertices of a 3-simplex): the first one is by manually defining the vertices of the simplex and the second, by finding a kind of minimal 3-simplex that contains the fractal. By allocating barycentric coordinates to each fractal point with respect to the vertices, every repositioning of the vertices leads to a fractal modification visible in real-time. Furthermore, the application offers other interesting features, such as editing the fractal by changing the IFS coefficients, saving files in a specific image format, rotation animation and continuous transformation of the fractal by continuous change of the parameters of some basic affine transformation. The application is written in JavaScript and uses the Three.js library.