Simulating a Kaleidoscope Using GeoGebra

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Figure 1. Screen capture of a kaleidoscope image.

Kaleidoscopes are geometric shapes with appealing symmetry, both reflective and rotational. Using GeoGebra, we can simulate a kaleidoscope, starting with one point or any small picture you like.

In the following construction, we start with one single point, Point A, which is reflected about the x- and y-axes, and the two lines that bisect the quadrants (namely, y=x and y=-x). Point A is also rotated around an octagon or rotated consecutively for 45 degrees.  

To add some visual effects, dynamic colors are used, which are random colors driven by the distance between the center of rotation and Point A.

Please feel free to drag Point A around and see if you can create your favorite images. At any time, please use Ctrl-F to remove the traces on Windows or click the Refresh button to return to the starting point.

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1. What if we just use the two axes and the two lines (y=x and y=-x)?

2. To what extent is the simulation above similar to a physical kaleidoscope?

3. It is pretty straightforward to construct in GeoGebra. What might small children think about it if they build their own?

Lingguo Bu @2009, Created with GeoGebra