The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius ands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.

Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.

"Fish," by Hamid Naderi YeganehThis image is like a fish. It shows 1,000 line segments. For i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-2cos(4πi/1000), (1/2)(cos(6πi/1000))^3) and (-(2/15)sin(6πi/1000), (4/5)sin(2πi/1000)). --- Hamid Naderi YeganehSep 16, 2015

"Boat," by Hamid Naderi YeganehThis image is like a sailing boat. It shows 2,000 line segments. For each k=1,2,3,...,2000 the endpoints of the k-th line segment are: (cos(6πk/2000)-i cos(12πk/2000))e^(3πi/4) and (sin((4πk/2000)+(π/8))+i sin((2πk/2000)+(π/3)))e^(3πi/4). --- Hamid Naderi Yeganeh Sep 16, 2015

"A Bird in Flight (2015)," by Hamid Naderi Yeganeh This image is like a bird in flight. It shows 500 line segments. For each i=1,2,3,...,500 the endpoints of the i-th line segment are: ((3/2)(sin((2πi/500)+(π/3)))^7, (1/4)(cos(6πi/500))^2) and
((1/5)sin((6πi/500)+(π/5)), (-2/3)(sin((2πi/500)-(π/3)))^2). ---
Hamid Naderi Yeganeh Sep 16, 2015

"10,000 Circles," by Hamid Naderi YeganehThis image shows 10,000 circles. For each i=1,2,3,...,10000 the center of the i-th circle is:
((cos(38πi/10000))^3, sin(10πi/10000)) and the radius of the i-th circle is: (1/3)(sin(16πi/10000))^2. --- Hamid Naderi Yeganeh Sep 16, 2015

"A Strawberry Lemon Spiral," by Frank A. Farris, Santa Clara University, CAInk jet on paper, 2015.

This image started life as a wallpaper pattern with symmetry group p2, based on a photograph of strawberries with a cut of lemon. After scaling it correctly, I applied the complex exponential map to wind it around the origin, creating a spiral of yellows, greens, and reds. I particularly enjoy how the lemon became a string of yellow wax beans, while the strawberries turned into peppermint candies. --- Frank Farris Sep 02, 2015

"Octahedral Globe from a Window," by Frank A. Farris, Santa Clara University, CAInk jet on paper, 2015.

This coloring of the sphere, based on a photograph of a stained-glass window by Hans Schepker, is invariant under the action of the octahedral group. I created it by mapping the sphere (and the group action) to the plane via stereographic projection and using known techniques for creating complex-valued functions invariant under groups that act on the plane. This image is part of a larger work, "Imaginary Planets." --- Frank Farris Sep 02, 2015

"Alternating Wood Bugs," by Frank A. Farris, Santa Clara University, CAInk jet on paper, 2015.

Had I used a source photograph whose colors reverse exactly when you turn it upside down, the image computed with these wallpaper waves would have exact color-reversing symmetry of type p4g/cmm. (See my book Creating Symmetry for explanation.) However, when you rotate my picture of a freshly cut pine stump, the colors only more-or-less reverse. This causes what I call "approximate color-reversing symmetry." The blond bugs marching northwest have the same outlines as the dark bugs marching northeast, but the details of the insides are quite different. --- Frank Farris Sep 02, 2015

"Random Walk on Sphere," by Daniel GriesPaths meander on a sphere with each small step taken at a random turning angle. The turn angle at each step is required to stay near the previous turn angle, as if the steering wheel of a car can only be turned slowly from one position to the next as the car drives forward. Computing random walks on a sphere has to be handled carefully with local coordinates so all random directions have an equal probability. Coded in Processing. --- Daniel Gries (Hopkins School, New Haven, CT)May 28, 2015