Circle or Square?

This is an Optical Art piece that lets your mind oscillate between seeing circles, squares or circles in squares. In some configurations it is obvious, in others that's a little more tricky.

The key concept that underlies this generative art piece is a mathematical algorithm that allows me to change a square array of dots into a circular arrangement. This is called circling a square.

The overall image is a regular 4 x 3 tessellation of "tiles" consisting of either circled or un-circled variations of a tile. Before I draw the image, I make three decisions. One, the choice which tile to use. Two, whether to shade the dots within a tile from the inside-out or the outside-in. And three, the background coloring. For the background color I chose either a uniform random color or one of four orientations of a linear gradient with its own random parameters.

In one version of a tile the positions of the dots are translated into a circle by the algorithm in the other version they are not translated. In both versions I scale the dots relative to their positions in the array that scale factor also determines their color, a shade of gray ranging from black to white.

It is possible for any iteration of this program to produce some crazy Gestalt effects. Enjoy.

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