Small business owner, puzzle designer, and artist, Tessellations Company

http://members.cox.net/fathauerart/index.html

tessellations@cox.net

Robert Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity. His artworks are created on a Macintosh computer, primarily using the commercial programs FreeHand and Photoshop. More recently, he has been exploring fractal arrangements of polyhedra.

"Angels and Devils" is a digital artwork based on a fractal arrangement of circles within circles. Two half-scale circles are placed within the starting circle and rotated by an angle of p/4 in opposite directions. These steps are then repeated in the smaller circles, etc. The motifs pay homage to one of M.C. Escher's most famous prints, "Circle Limit IV", which also contains angel and devil motifs. Escher's print is based on hyperbolic geometry, which distorts the motifs as they get smaller. All of the tiles in "Angels and Devils" are similar in the Euclidean plane.

“ Fractal Tree No. 3 ”

"Fractal Tree No.3" is a black-and-white digital artwork constructed by graphically iterating an arrangement of a small portion of a photograph of a tree. The original photograph was digitally altered to allow smooth joining of the smaller copies. In addition to being scaled down, the three smaller copies added with each iteration are all rotated by varying angles, and one is reflected as well. A sufficiently large number of iterations is performed so that the image is indistinguishable from the image that would result after an infinite number of iterations. In this particular design, the iteration rules result in considerable overlap of the branches. One of the three smaller copies is lightened with each iteration, providing an illusion of depth in the overlap regions.

“ Fractal Tree No. 4 ”

"Fractal Tree No.4" is a black-and-white digital artwork constructed by graphically iterating an arrangement of a small portion of a photograph of a bush. The original photograph was digitally altered to allow smooth joining of the smaller copies. In addition to being scaled down, the three smaller copies added with each iteration are all rotated by varying angles. The spiral forms result from the repeated combination of shrinkage and rotation. A sufficiently large number of iterations is performed so that the image is indistinguishable from the image that would result after an infinite number of iterations. In this particular design, the iteration rules result in considerable overlap of the branches. One of the three smaller copies is lightened with each iteration, providing an illusion of depth in the overlap regions.

“ Fractal Tree No. 5 ”

"Fractal Tree No.5" is a black-and-white digital artwork constructed by graphically iterating an arrangement of a small portion of a photograph of a rosebush. The original photograph was digitally altered to allow smooth joining of the smaller copies. In addition to being scaled down, the three smaller copies added with each iteration are all rotated by varying angles, and one is reflected as well. The rugged appearance of the thorny stalks is juxtaposed with the light feathery appearance of the overall fractal. A sufficiently large number of iterations is performed so that the image is indistinguishable from the image that would result after an infinite number of iterations. In this particular design, the iteration rules result in considerable overlap of the branches.