Robert Fathauer

This image was created by reflecting and overlapping four copies of a photograph of Lower Antelope Canyon, a sandstone slot canyon near Page, Arizona. Working in Photoshop, the levels of each color channel were adjusted separately in different regions of the image to heighten the value and color contrasts.

A starting knot was created that possessed sufficient geometric regularity to allow iterative replacement of a portion of the knot with a scaled down copy of the knot. This starting knot had nine crossings and was configured as a trefoil knot nested inside another trefoil knot. Six iterations were carried out in order to achieve the knot shown here. The path of the strand, specified as a series of Cartesian coordinates, was smoothed out so that strand in the final knot curves gracefully, as opposed to being a series of straight line segments that change angle abruptly. The knot was constructed using the program KnotPlot and then exported to PhotoShop for touching up.

A starting knot was created that possessed sufficient geometric regularity to allow iterative replacement of a portion of the knot with a scaled down copy of the knot. Three such iterations were carried out to obtain the knot shown here. The path of the strand, specified as a series of Cartesian coordinates, was smoothed out so that strand in the final knot curves gracefully, as opposed to being a series of straight line segments that change angle abruptly. The knot was constructed using the program KnotPlot and then exported to PhotoShop for touching up.