Writing similarity transformations

One cool trick you can do with the IFS visualizer is to use one function with the depth set to 1 in the deterministic algorithm. This allows you to visualize the affect that one function has and allows you to practice entering more complicated functions. For example, here's now I can set it up to visualize the affect of a single scaling transformation:

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Try this trick to visualize the affects of the following similarity transformations:

1. A scaling by the factor $1/4$ about the point $(1,1)$.
2. A scaling by the factor $1/2$ about the origin followed by a rotation through the angle $45^{\circ}$.
   • Does it matter what order we do that in?
3. A scaling by the factor $1/2$ about the point $(1,0)$, followed by a reflection about the $y$-axis, followed by a shift to the right by $1$ unit.
   • Does it matter what order we do that in?

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Scaled by the factor of $1/4$ about the point $(1,1)$. You can't see the axes because when the polygon was scaled about the point $(1,1)$ it was moved off of the axes.