I'm always fascinated by things that are symmetric. In symmetrical things we see beauty and thereby mathematics. It is therefore a quest and adventure for an inquisitive mind to go deeper and deeper to study the building blocks of things that are symmetric. The images that I produce show the ubiquity of mathematics and how mathematics is a key to understand the nature that we live in, in particular, and how it unlocks the secrets of our universe in general.

The usual elementary functions and their compositions can generate sophisticated graphs which are shown. The structures (or patterns) are superimpositions of polar surfaces resulted from several compositions of tilts and turns on the coordinate axes in three dimensions. When they are viewed from a different turn and tilt they generate a totally different, fascinating structure.

The structures are a few from my collection, which numbers more than 70. For those who are interested to see them, check my website and click on the gallery button.

---Dejenie A. Lakew, Virginia State University

6 files, last one added on Feb 28, 2008

I love experimenting in the fuzzy overlap between art, mathematics, and programming. The computer is my canvas, and this is algorithmic artwork--a partnership mediated not by the brush or pencil but by the shared language of software. Seeking to extract and visualize the beauty that I glimpse beneath the surface of equations, I create custom interactive programs and use them to explore algorithms, and ultimately to generate artwork.

In the world of chaotic dynamical systems, minute changes in initial conditions produce radically different results. The interface of my software gives me hooks into the algorithms and allows me to exert some control. But there is always tension - between the computer and me, between simplicity and complexity, and between problem solving and spontaneity.

Art and mathematics, the right brain and the left, are inextricably linked in this work. My art depends on mathematics, yet simultaneously illuminates and unravels its beauty. I am an explorer who uncovers something extraordinary, bringing into view that which was always there to be discovered.

---Nathan Selikoff

4 files, last one added on Feb 26, 2008

These images illustrate a variety of kinds of symmetrical figures; most were produced for "The Symmetries of Things," written with John H. Conway and Heidi Burgiel (A.K. Peters, 2008), using a variety of proprietary software tools.

I have been interested in geometry, pattern, and mathematical illustration of one form or another since I was a child. Abstraction is the basis of the power of mathematics, but too often we forget that mathematics is also a descriptive language, with meaning anchored in intuitive experience of the world around us. How many students emerge from, say, an undergraduate linear algebra course for math majors, knowing full well proofs of the existence and characterization of eigenspaces and eigenvalues, having no simple, clear idea of what such objects might look like?

Though I am as seduced by abstraction as any research mathematician, I am drawn to mathematics I can see and touch; mathematical illustration, carried out in a graphically rigorous manner, is a natural extension of my work as a mathematician--and indeed may be more fundamental to me.

---Chaim Goodman-Strauss, University of Arkansas

9 files, last one added on Jan 31, 2008