Mathematical Art

Diagnosis Cancer, Titia van Beugen, Dutch mathematical artist.
She died of breast cancer in 2010.

“Mathematics, rightly viewed, possess not only truth,
but supreme beauty--a beauty cold and austere, like
that of sculpture.”  --Bertrand Russell
                                         British author, mathematician, & philosopher (1872-1970)

Very often artists, like the majority of other human dwellers upon this earth, are adverse to mathematics. Art and math would seem to be polar opposites--output from opposite hemispheres of the cerebral cortex. Few artists might argue with that, though, today, quite a number of mathematicians would. As a young man, I was endlessly fascinated by architecture (still am) but I was never very good at higher mathematics. I hated algebra, was barely on speaking terms with geometry, and terrified by calculus and trigonometry. Slide rules (remember slide rules?) always seemed like more trouble than they were worth, and I was born too soon to benefit academically from pocket calculators. Had all this not been the case, I might have become an architect rather than an art instructor/painter/writer.



The Meeting of Solomon and Sheba,
1450-52, Lorenzo Ghiberti, east door of the
Florence Baptistery--perfect perspective.

Actually the relationship between math and art is long and surprisingly intimate. By the 14th century there was a whole book on perspective by a mathematician named Alhazen, though it took mathematically inclined Florentine artists such as Lorenzo Ghiberti and his friend, Filippo Brunelleschi, to translate his by-the-book formulas into practical applications and teach them to all the mathematically adverse Renaissance artists to follow. Of course, architects such as Brunelleschi and Ghiberti, though artists, have, by necessity, embraced mathematics far more readily than did painters (for reasons outlined above). 

 And that's pretty much where things stood for five hundred years--mathematicians occasionally toying with art, but few artists, like myself, having more than a passing acquaintance with the underlying formulas governing the linear perspective they employed daily. Then came computers. Mathematicians, had, in fact, been graphing their obscure algebraic equations for centuries, but the calculations, not to mention the crudity of their tools, made such efforts way too time consuming to be more than a quickly passing fancy. Mathematicians had better things to do with their valuable time than draw pictures.

 

A Mandelbrot set, featuring
virtually infinite complexity.

With computers, first there was Mandelbrot--Benoit Mandelbrot (02-24-12), an IBM mathematician who, in 1979, with his pioneering work in fractal geometry, was among the first to grasp the fact that the ever-increasing speed of a digital processors erased the primary obstacle in the marriage of art and higher mathematics. But Mandelbrot was a mathematician first, and only an artist, of sorts, more or less by accident. But as computer technology eventually began to rely upon various graphic interfaces, the intricacies of Mandelbrot receded into the realm of fascinating oddity to be replaced by the practical mathematical and artistic demands of counting, collating, and coloring pixels for human consumption. 



Roots grown from multiple seeds using a constrained 3D DLA algorithm,
Paul Bourke, New Zealand mathematical artist



Frabjous, George Hart,
American mathematical sculptor

If you look at today's mathematical artists you find that, like Mandelbrot, they are virtually all mathematicians first, having developed a secondary interest in art. There's even a virtual math museum. Few, if any, of this new breed of artists even own a paintbrush, though some mathematical sculptors rely on traditional tools in giving substance to their computer-aided designs. Like all good artists, mathematical artists create work of great diversity visually, yet it is mostly of an abstract nature often utilizing a great degree of symmetry while having the "cold and austere" beauty Bertrand Russell found so enthralling.

The Apocalipse (Revelation), Anatoly Fromenko, Russian mathematical artist,
work not totally devoid of representational content.