'Who visits the Temple of the Peach? My first step in going there was to paste the Hyperbolic Peach pattern that I used to illustrate non-Euclidean geometry around the inside of a cylinder, the temple wall.The giant globe holder with its peach medallion holds a sphere decorated with another pattern made from the same peach photograph, which is propped on the floor. Photoshop allows me to tell that floor to be highly reflected. I had to let the ray-tracing software run for a day to produce this scene.'
'Everyone working in symmetry owes a debt to M.C. Escher, whose wonderful figurative drawings illustrate virtually every type of known plane symmetry. This set of four panels is meant to honor Escher’s great Metamorphosis series, woodcut prints with the largest almost 7 meters long.In Metamorphosis II, Escher’s magic turns lizards into bees into fish into birds; and all by hand. My technique for morphing requires much less cleverness: I simply blend from one pattern into another.
In this set of panels, I show every type of wallpaper symmetry with either 3-fold or 6-fold rotational symmetry, making this something of a wallpaper sampler. (Which pattern has the same type as “Autumn Moths”?)'
'The story of symmetry and color-reversing symmetry on the sphere is quite similar to the story on the Euclidean plane. It’s just a sort of round plane. The symmetries are those of the Platonic solids: tetrahedron, cube/octahedron, and dodecahedron/icosahedron.There are actually seven different types of polyhedral symmetry, allowing different mirror symmetries, as exemplified by the seven larger globes in the image.
The smaller globes show color-reversing symmetry. With any colorreversing pattern we can think about what symmetries would be present if we took a color and its negative to be the same thing, as if antisymmetries were actual symmetries. On each blue path, the smaller globe has the same symmetry type as the globe at the start of the path (moving down and to the right), and would have the symmetry type of the globe at the end if you were to identify colors and their negatives.'
'The pattern in the background of this image does not exactly have color reversing symmetry. The source photograph of granite and moss is only vaguely color-reversing when you turn it upside down: the greens turn into grays. Still, when I used it with a formula that would yield color reversing symmetry, it led to the two similar-but-different shapes: frogs and bugs. Then I wound the pattern onto a sphere in a spiral pattern. I added the purple haze by hand, using Photoshop.'
'Color-reversing patterns are also called 2-color patterns because you can make them with just two colors. Why stop at two?First I turned a photo (of a beautiful steak and a smear of yams) into a collage where the colors shift by a third of the hue wheel when you turn it by 120°. Then I used a particular mathematical formula to make a pattern where the whole pattern has that same property: You can turn it 120° about various points and all the colors shift hue perfectly. Of course, it’s crazy to look at.'
'The big surprise about wallpaper patterns is that there are exactly 17 types. After making many examples of each type, I still return to the type of this pattern as a favorite; it’s called p31m. Notice the three-fold rotational symmetry, but also the alternation of mirror symmetry with three-way pinwheels. For me, this gives a beautiful balance of sameness and variation. It’s symmetric, yet organic.I took the source photograph on an autumn day, hiking in the golden hills above San Jose, CA. This piece shows that interesting patterns can arise from photographs with rather limited color palettes.'
Mandalas invite the eye to wander in a circle of spiral patterns, finding places where the design repeats itself. In each pattern, we can find the panes of the stained glass window that gives its colors to the design. Each mandala was created using a mathematical formula to reference pixels in the source photograph of the window, as well as its negative. Both mandalas have five-fold rotational symmetry, an uncommon choice in mandala design, but one that echoes the symmetry of the window, which was made from my design by Hans Schepker.
A square canvas work with a photograph of the back of a man's head and neck glued onto the surface. Blue, green, and yellow paint are dried thickly and appear to come out of the two-dimensional photograph of the head. Above is written: 'THEO PELMUS MADE IN OTTAWA' and below: 'OUT OF MY EARS 2007.'
A black-and-white print of a religious toned scene. A man with a bird perched on his hand leads a family with a small child. There is a large circle of light behind his head, and an emaciated figure floats prostrate above him. There is a small crowd of people, animals, and other creatures rejoicing and playing instruments below them.
A black-and-white print of a goblin like man holding a candelabra and leading a family with a small child. There is a full moon lighting the scene with a black cat sitting in it. A small, winged figure stands in the corner of the frame looking onward.
A black-and-white print of a dramatic, religious toned scene. A family sits on the ground with a small child collapsed in a woman's arms and a man reaches toward the sky in desperation. In the background, another family looks onward and a small bird flies above their heads.
Ceramic figurine of a woman sitting on a stool with a puppy on her head holding a lunch container in her lap. She is wearing a yellow jacket with green pants that match the stool.
Ceramic figurine of a woman sitting on a stool with a puppy on her head holding a lunch container in her lap. She is wearing a yellow jacket with green pants that match the stool.
