They must also enter the coordinates of these points to create their own fractal generator. We will have the user calculate with the aid of a help file what the affine transformations are. The program then checks their work. This way we are teaching the user about fractals. Understanding what fractals are and how to create them is the main background we need to start this project.
Fractals are complex objects with self-similarity, which are created using some fixed algorithm.
This algorithm is an application of a set of affine transformations, or functions, on a set of points, lines, or 2-dimensional objects. Affine transformations can be very complex and take a long time to calculate on paper, even for simple cases. This is why we would like to create a computer program that will calculate these functions. Iterating affine transformations create fractals because of the Contraction Mapping Theorem. This theorem states that if a contraction mapping, f, is infinitely applied on a collection of points, then these points converge to a more condensed set of points.