A novel software application for interactive affine transformations of fractals

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 controllable and visible, done by dragging and dropping three predefined non-collinear points, exploiting the full potential of high quality fractal rendering in real-time. The affine transformations are enabled by assigning barycentric coordinates to the points that represent the image of the fractal attractor with respect to the three above mentioned points and thus relating the fractal to the points. Besides this main purpose of our application, many other features are offered: modifying specific parameters in the IFS code, gradually changing one or more parameters in the IFS code to follow the continuous transformation of the fractal attractor as a form of animation, coloring fractals, saving files in different image formats for post-processing, exporting and importing IFS parameter files and performing fast basic transformations to the fractals with the hotkeys option. Also, the application allows finding vertices of a kind of triangle with minimal area that contains the fractal, which form an affine basis. The practical use of such affine basis in modeling particular fractal is that the fractal is in the convex hull of the last affine basis, which makes the modeling more governable.