Periodic images from the kaleidoscope

It is still cold outside and the soil is frozen. Thus I have not much to do in the garden and a lot of time for this blog.

In the previous article “How to program an ideal kaleidoscope” I have tried to explain how I programmed a virtual kaleidoscope. Here I want to show you some results for kaleidoscopes with three, four and six-fold rotational symmetry. These symmetries give periodic images.

Two reflections at different mirrors make a rotation by double the angle between the mirrors. Thus if the three mirrors form an equilateral triangle we get rotations by 120 degrees. This results in three-fold rotational symmetries and periodic images:

gleichs

Image from three mirrors arranged as an equal sided triangle.

If the angle between the mirrors are 30, 60 and 90 degrees we get rotations by 60 degrees, hexagonal rotational symmetry and periodic images:

dreieck30-60-90

Kaliedoscope with three mirrors at angles of 30, 60 and 90 degrees.

Finally, mirrors at angles of 45 and 90 degrees make four-fold rotational symmetries:

dreeck45-90-45

Image from three mirrors at angles of 45 and 90 degrees.

Thank you for looking at my work. I am dreaming of sunshine and gardening.

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