Fixing a Fixed Point

A simple example of a fixed point theorem.

A rectangle on a brown background is repeatedly transformed by a composition of shrinking, rotating, and translating; the successive images of the rectangle are colored alternately black and white. There can be a point on all the smaller images that is directly above the same point on the largest image: the limiting point of the transformation. Drag the locators to control the three parameters of the transformation: the first locator controls translating and the polar coordinates of the second locator control rotating and scaling.