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 bands, 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.

668 files in 43 albums with 0 comments viewed 775,100 times
 Robert J. Lang :: Origami The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. We can group these intersections into roughly three categories: Origami mathematics, which includes the mathematics that describes the underlying laws of origami; Computational origami, which comprises algorithms and theory devoted to the solution of origami problems by mathematical means; Origami technology, which is the application of origami (and folding in general) to the solution of problems arising in engineering, industrial design, and technology in general. One genre blends into another. Origami math defines the "ground rules" for computational origami's goal of solving origami design problems (and quantifying their difficulty). The results of computational origami, in turn, can be (and have been) pressed into service to solve technological problems ranging from consumer products to the space program. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 40 years, I have developed nearly 600 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality. My website includes galleries of my designs, crease patterns, schedule of my lectures, appearances and exhibitions, commissioned works, and more on the science of origami. --- Robert J. Lang 26 files, last one added on May 08, 2018Album viewed 12636 times
 2018 Mathematical Art Exhibition The 2018 Mathematical Art Exhibition was held at the Joint Mathematical Meetings held in San Diego, CA. Here on Mathematical Imagery is a selection of the works in various media, including recipients of the 2018 Mathematical Art Exhibition Awards: "A Gooseberry/Fibonacci Spiral,” by Frank A Farris, awarded Best photograph, painting, or print; "Dodecahedral 11-Hole Torus," by David Honda, awarded Best textile, sculpture, or other medium; and "Excentrica" by Ekaterina Lukasheva, Honorable Mention. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. Click on the thumbnail images to view larger. 39 files, last one added on Apr 27, 2018Album viewed 990 times
 Fractal Experiments :: Stephen Ren I had always known the beauty and power of mathematics, but after discovering the connection between complex numbers and fractals, I became deeply fascinated in how fractals express and reflect that beauty. Whereas mathematical beauty often lay in abstract concepts and elegant proofs, fractals bring the beauty of mathematics plainly to the surface, unobscured and for all to see. Following my curiosity, I wrote a Java program to generate and explore fractals, as I find that creation and experimentation often brings about a deeper sense of understanding than just observation. At the time I had just tackled a number theory problem regarding tetration (super-exponential functions), and decided to generate fractals based on that. After generating the fractal, I experimented with changing my rendering method a little bit, and to my surprise, a completely new form of fractals emerged, which is shared here. The base function for all these images is still simply standard tetration, the only difference being that color (or shade) of each pixel (representing a point in the complex plane) is dependent on the maximum reference angle of that point as tetration is repeatedly applied, rather than whether or not the magnitude of that point would increase without bounds, the latter being what standard tetration fractals are made from. I was astonished that such a small change would produce such intricate results that were quite different from normal tetration fractals. No matter how much I think about it, I am still amazed that the basis of these images is purely mathematics, and I hope to share that beauty here in this gallery. --- Stephen Ren, North Hollywood, CA 7 files, last one added on Nov 22, 2017Album viewed 1033 times
 2017 Mathematical Art Exhibition The 2017 Mathematical Art Exhibition was held at the Joint Mathematical Meetings held in Atlanta, GA. Here on Mathematical Imagery is a selection of the works in various media, including recipients of the 2017 Mathematical Art Exhibition Awards: Fractal Monarchs," by Doug Dunham and John Shier, was awarded Best photograph, painting, or print; "Torus," by Jiangmei Wu, was awarded Best textile, sculpture, or other medium; and "AAABBB, two juxtapositions: Dots & Blossoms, Windmills & Pinwheels," by Mary Klotz, received Honorable Mention. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name. 30 files, last one added on May 09, 2017Album viewed 2164 times
 Frank Farris :: Seeing Symmetry I'm particularly interested in visualizing mathematics and giving talks on mathematics and art. Many of my digital works, some of which are made into fabric and wallpaper, are based on photographs of everyday scenes and objects. --- Frank A. Farris, Santa Clara University 15 files, last one added on Jul 05, 2017Album viewed 3889 times
 Daniel Gries: Digital Works After receiving a Ph.D. in mathematics at Ohio State, I taught for several years at Merrimack College in Massachusetts, followed by a visiting position at Hamilton College, before settling into teaching mathematics and computer science at Hopkins School in New Haven, Connecticut. Although I teach mathematics for a living, I am also passionate about coding, music, and visual arts. I have helped to maintain the Flash tutorial site flashandmath, and more recently my own HTML5 Canvas and JavaScript blog, rectangleworld. --- Daniel Gries (Hopkins School, New Haven, CT) 9 files, last one added on May 28, 2015Album viewed 1902 times
 Simon Beck's Snow and Sand Patterns I create geometric patterns in the snow, walking along the frozen lakes of Savoie, France in snowshoes. On average the works take about 10 hours to really do it properly, some are a little unfinished, if my feet get cold or hurt too much. The setting out is done using handheld orienteering compass and distance determination using pace counting or measuring tape. Curves are either judged or arcs of circles are made using a clothesline attached to an anchor at the centre. Designs are chosen from the world of geometry. The Koch curve and Sierpinski triangle in this album are among my favorites. The works are very large (the size of several soccer fields), and many of the mathematical patterns appear 3D, especially when viewed from above. more recently I've also created patterns in the sand. --- Simon Beck 9 files, last one added on Aug 19, 2014Album viewed 8962 times
 Carlo Séquin :: Mathematical Images Since high school I have been fascinated by geometry. I enjoyed constructing the more complicated Platonic solids with ruler and compasses, as well as reading about the 4th dimension. While at Bell Labs in Murray Hill, I was introduced to the field of Computer Graphics, and later developed the Berkeley UniGrafix rendering system, so that I could depict objects more complex than I could build. Since then, the focus of my work has been on computer-aided design (CAD) tools -- for engineers, architects, and artists. When creating abstract sculptures I see myself as a composer in the realm of pure geometry. The artistic achievement then lies in finding a procedural formulation that can reflect the inherent symmetries and constructive elegance that seems to lie beneath many sculptural master pieces as well as at the foundations of the physical laws of our universe. --- Carlo Séquin 16 files, last one added on Mar 18, 2013Album viewed 3965 times
 Mathematical Concepts Illustrated by Hamid Naderi Yeganeh One of my goals is to create very beautiful images by using mathematical concepts such as trigonometric functions, exponential function, regular polygons, line segments, etc. I create images by running my program on a Linux operating system. --- Hamid Naderi Yeganeh 17 files, last one added on Mar 23, 2016Album viewed 5078 times
 2016 Mathematical Art Exhibition The 2016 Mathematical Art Exhibition was held at the Joint Mathematical Meetings held in Seattle, WA. Here on Mathematical Imagery is a selection of the works in various media, including recipients of the 2016 Mathematical Art Exhibition Awards: "45 Poppies," by Karl Kattchee was awarded Best photograph, painting, or print; "Sword Dancing," by George Hart was awarded Best textile, sculpture, or other medium; and "OSU Triptych No. 2," by Robert Orndorff received Honorable Mention. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name. 31 files, last one added on Jun 23, 2016Album viewed 3726 times
 Anne M. Burns :: Gallery of "Mathscapes", Complex Flows and More Computers make it possible for me to "see" the beauty of mathematics. The artworks in the gallery were created using a variety of mathematical formulas. --- Anne M. Burns 21 files, last one added on Oct 22, 2015Album viewed 28625 times