My interest in being an artist comes from growing up in a close-knit community in Central New Jersey in the early 1950s as the son of Jewish chicken farmers turned landscapers.  My parents’ switch to horticulture was a true gift to me, nurturing a fascination with exotic plants and gardens beginning in my elementary school years, an attachment that has remained with me to this day.  Indeed, it is photographic images of the plants that I grow in my own exotic garden that serve as the basis for much of my digital art.  I genuinely love to look at and cultivate plants and admire their beauty, but even as a very young child I also had a passion for math and science that sealed my commitment to science at a very early age.  Today, I am a practicing biophysicist, but I have also developed as a mathematical artist due to a seminal family tie.  My brother Gene is a classically trained artist in oils and watercolors, and by the late 80s he had also become a digital artist, using available tools such as Photoshop and Painter to create representational paintings from photographs. When our first child came in 1992, he urged me to try fractal style painting with the computer because I am good at math and he said it might relax me. Up to that point I, like a lot of biologists, was an indifferent computer programmer.  Now I had a second chance, and I dived into learning proper structured programming by building dynamic painting programs.  Gradually, this focus on computer programming proved invaluable to my professional scientific work.  But for 10 years every night I also worked very hard on digital imaging problems my brother gave me, until I finally turned exclusively to scientific programming at the turn of the century. In the years since, slowly cooking in my subconscious was a scheme for a very large and complex color and space manipulation engine. It took me years to finally sit down and write the code, and I am continually expanding it, but it has been fully operational for some time, allowing me to create a wide array of representational, impressionist, surreal and abstract images purely through the use of mathematics.  

Philosophy as a Digital Artist




My philosophy of Digital Art is that it represents another form of painting. Usually, instead of using brush and paint and canvas, the digital artist uses the virtual easel of the screen and the tools available to manipulate bitmap files (Adobe Photoshop, Painter, etc.) to construct the image he or she is imagining. What I do is partially within that mold, but with a fundamentally different twist. Except for changing file types and printing, all actual manipulation of my images is done exclusively with a large software engine that I have written and continue to expand. A crude analogy would be a traditional artist who also creates his or her paints, brushes and canvas from raw materials. Yet that comparison is still profoundly misleading because in reality I am exploring the power of my complex multilevel mathematical equations to ferret out a small sample of the virtually infinite patterns hidden in the photographs I use as raw material. Part of the art is the images created, part of it is the invention of a continuously expanding image transformation engine. In this way I demonstrate that hidden in ordinary photographic images of flowers, landscapes, everyday objects, animals and humans is an endless array of magical forms waiting to be birthed. This has led me to focus on four artistic goals. First, I try to demonstrate that mathematical systems, properly crafted, can produce a much richer set of artistic images than the hyper-geometric, fractally generated images that typically characterize mathematical art in the minds of most people. A crucial element of this first goal is to create textures and abstractions that are as “painterly” as possible. A second goal is to explore as wide a range of mathematical systems as I can utilizing a rich mixture of the classic elementary functions, differential difference equations, modified trigonometric type functions and recursion, to continuously broaden the range of images I can create. A third goal is the hybridization of images that are seemingly incompatible, e.g. flowers and printers, Dutch windmills and people, cafes and vases of silk flowers. Because the hybridization is part of the complex transformation process it often produces startlingly unexpected results. Finally I have an overarching goal of producing images that are compellingly beautiful while simultaneously exploring the limits of beauty as they relate to mathematically generated hybridizations and transformations. This last goal flows naturally from my love of both gardening and math. We know that many of the most precious things in our lives are the gifts of beauty bestowed by the natural world, e.g. flowers, trees, butterflies and birds. I try to explore the limits of that innate beauty in my work. 

How do I do it?


First, a description of digital images. Digital images are made of pixels, little squares of color on your computer screen. A pixel can emit red light, green light and blue light at independent intensities for each color. There are 256 levels of intensity for each color and by emitting at different intensities one can create every color that the human eye can see and more: 2563or 16,777,216 colors. In the computer’s memory this information is stored as a bitmap, a long string of numbers. Each pixel is represented by the three values, integers 0 to 255 as described above in the order blue, green, then red. The display system knows to treat successive blocks of these triplets as horizontal lines in the image. Thus, each pixel has numerous numbers associated with it. In my system I use 9, although rarely all of them at once. They are the red, green and blue values, the x value, i.e. the number of pixels in from the left edge of the image, the y value which is the number of lines of pixels from the bottom of the image, the number of pixels from the beginning of the image, and the cyan, yellow and magenta values of the pixel. Sets of these numbers are fed into a first set of algebraic equations which I choose from several hundred sets and these generate new x,y and sometimes blue green and red values. These are then fed into a second set of equations that I define from an unlimited set of possibilities, then a third and sometimes a fourth equation set, each from a large collection of such sets. The final output is a new x,y blue, green and red value in a new transformed image. I can do this with one image or while hybridizing two images at once, either original photos or previously transformed images or both. To reiterate, all of the painting is done by the equations I have chosen  after I have input the coefficients and exponents to control the equationsd. However, unlike fractal art, I start with real world images and transform them, exploring hidden artistic elements of the physical world through mathematics.