An iterative hexagonal kaleidoscope

schema

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:

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

stonesauto

This entry was posted in Fractals, Kaleidoscopes and tagged , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s