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assignment_0 - 6.837 Introduction to Computer Graphics...

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Unformatted text preview: 6.837 Introduction to Computer Graphics Assignment 0: Iterated Function Systems (IFS) Due Wednesday September 10, 2003 at 11:59pm The goal of this assignment is to get familiar with C++ and with two simple libraries that we will use for linear algebra and images. The incidental goal is also to have fun with bizarre fractal objects: IFSs. Figure 1: Barnsley’s fern IFS are self-similar fractals: a subpart of the object is similar to the whole. The classic example of an IFS is Barnsley’s fern, where each subpart of the fern is exactly the same as the whole fern. IFS are described by a set of aﬃne transformations (rotations, translations, scale, skew, etc.) These transforma- tions capture the self-similarity of the object (see Figure 1). IFS can be defined in any dimension, but we will play with two-dimensional ones. Formally, an IFS is defined by n aﬃne transformations. Each transformation, f i , must be contractive: The distance between points must be reduced. An attractor of the IFS is the object such that A = f i ( A ). A is unchanged by the set of transformations: It is a fixed point....
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assignment_0 - 6.837 Introduction to Computer Graphics...

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