Iterative subdivision of a hexagon. The black lines show the mirror lines of the resulting kaleidoscope.

We can use the geometry of the last post differently. Draw inside a hexagon two equal sided triangles with the same corners as the hexagon. Then the intersection between the triangles gives a new smaller hexagon. Repeating this we get a series of shrinking hexagons. The sides of the triangles and the hexagons can be used as mirror lines. Together with the lines between the center of the hexagons and their corners and the middle of their sides we get a good kaleidoscope.

The results depend much upon the original photo. From a shrub of peonies I get this:

The courtyard of our school gives a much more geometrical picture:

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