Complexity Explorer Santa Fe Institute

Affine Transformations

This model introduces linear affine transformations, by having the user experiment with applying various scaling, rotation, and translation operations to a point in the plane. A translation is performed on a point via vector addition. Then, a point can be scaled by multiplying it by a scalar constant. Finally, a point can be rotated by multiplication by a rotation matrix. In our representation, the scaling of the point is incorporated into the matrix multiplication, so that a single operation scales, reflects, and rotates the point. The user can see the transformation matrix resulting from their desired scaling and rotation, and the matrix multiplication and vector addition operations are shown in the output window.
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