Simple example of a rosette with two-color symmetry

To keep things simple I am creating rosette with six-fold rotational symmetry. The mapping functions are, using polar coordinates: X = r³ cos(6*φ) and Y = r³ sin(6*φ). An input image of a single butterfly results in 6 distorted butterflies:

The black wings make a dominant shape resembling a propeller with 6 blades.

For a two-color symmetry I use a control function of three-fold rotational symmetry
W = r cos(3*φ).

Using simple color inversion I get:

Clearly, this image has only three-fold rotational symmetry. The black wings become white in the parts with the inverted color and this destroys the propeller shape. The image now has two rather disparate parts.

With the improved inversion of my last post, that only changes the hue and not the grey part, I get a subtler effect:

The propeller shape is not destroyed and the image seems to be more coherent. We see that the rather bright yellow of the centers of the flowers becomes a much darker blue. Thus, even with this method we get changes in brightness. The false colors are interesting or disturbing – that depends on your taste.

This entry was posted in 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