rosettes with glide reflection

For a rosette of p-fold rotational symmetry you have an equivalent to the glide reflection symmetry of a fries. It is a rotation by an angle of π/p around its center together with a reflection or  rather inversion at r=1. Thus the mapping functions have the condition f(r,φ)=f(1/r,φ+π/p), which results in




where I have used that cos{lp(φ+π/p)}=cos(lpφ+lπ). Using a photo of a yellow dragonfly I get this result of six-fold rotational symmetry:


Note the yellow horseshoe like shapes. The glide reflection makes that there are 12 copies, six opened towards the center and six opened outwards. Together they form a prominent star.

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

Leave a Reply

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

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

Google+ photo

You are commenting using your Google+ 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 )


Connecting to %s