Which came first in your life, the science or the art? 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 grew 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. So I left the farm for a degree in biology at Caltech. Then off to grad school in neurophysiology at Columbia. I left that program for personal reasons. Four years later I started again studying the low temperature physics of freezing in trees. This time I finished my PhD in that topic at the University of Maryland at College Park. Subsequently, I worked on the physics of frozen blood cells, fruit fly mortality, protein stability and for the last 20 years the physical chemistry of protein chromatography. Today, I am still a practicing biophysicist marketing chromatography technology I co-invented and now working on a broad spectrum anti-bacterial and anti-viral formulation, but I have also developed as a mathematical artist due to a seminal family tie. My late brother Gene was 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 elegant 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 many biologists, was a barely profficient computer programmer. Now I had a second chance, and I dived into learning proper structured programming by initially building screen saver painting programs. I soon switched to working every night on digital imaging problems my brother gave me, until finally I turned exclusively to scientific programming at the turn of the century, and this focus on computer programming proved invaluable to my professional scientific work. Yet 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 seven years, allowing me to create a wide array of representational, impressionist, surreal and abstract images purely using mathematics.

What materials do you use to create your artworks? All the software used to create my images has been created by me, including the resize software that allows me to print very large format images with exquisite fidelity (I have patented the resize software). The software is a mathematical painting engine that I control through a GUI. What the software is doing under my direction can be envisioned accurately as follows. Imagine an image made of wet paint (in my program this is either a digital photograph or previously transformed image or hybrids thereof). The artist takes a brush and begins to swirl the paint around or takes a dab of paint from one part of the image and transfers it to another part. Now imagine that the tip of the brush is so fine, and the image is discerned at the microscopic level, such that the artist can control the movement of each individual dye element in the paint (each pixel in a digital image). Finally, imagine that the movement of the brush holding each dye element is controlled by complex patterning strategies the artist conceives. That is very close to what I do with my main engine. After each element is algorithmically moved to its new location a second mathematical transformation of the element's colors can also be simultaneously initiated if I so choose as I set up the painting run. Because I can control the parameters in the equations to one part in a billion billion, I can manipulate my images with great precision and can systematically alter the images to try to achieve an acceptable esthetic. In addition, a separate part of my system allows me to do extremely complex color transformations on each pixel using mathematical transformations of the colors in the pixels immediately surrounding it. This allows me to expose amazing hidden patterns even in unremarkable images. In more technical detail, the generative painting program has two main components. The primary component is equivalent to a microscopic brush. A 24 bit full color rgb bitmap (or two) is loaded into memory. If two bitmaps they are hybridized according to channel-by-channel proportions set by the user in the GUI. Each pixel is taken as a point in a multi-dimensional space. The axes are red, green, blue, cyan, magenta, yellow, luminosity, x ,y, number of pixels from the beginning of the map, number of bytes from the beginning of the map, all of the aforementioned color values scaled, respectively, to the maxima of the x and y values of the map for a total of values in up to 24 dimensions. A subset of values for each pixel in turn is fed into a first set of equations chosen in the GUI. The output of that set is fed into two 10 term power functions in x and y respectively. The output of that set is fed into a third set of equations chosen in the GUI and the output of that identifies a calculated new x and y. Then that pixel at the new location in the reference map replaces the pixel in the reference location in the target map. Additionally, the red, green and blue values of the replacement pixel can be transformed simultaneously as controlled from the GUI and calculated in the equation sets. All constants of the equation sets, coefficients and exponents are chosen as initial inputs in the GUI. Thus, the process is akin to taking a brush with a one pixel wide tip and, pixel by pixel, swirling each pixel to a new position, and sometimes subjecting its colors to mathematical transformation as well. The secondary component of the painting engine feeds summed data from mathematical transformation of the r,g,b values and sometimes position values from each of the 8, 16 or 24 pixels around each pixel into equation sets to calculate new r,g,b values for the central pixel, i.e. purely a color modifier. Again, coefficients and exponents are controlled from the GUI. The range of mathematical functions is large: all of the elementary functions, numerical differential equations , numerical integral equations, power functions, recursive versions of all equations and logical filters based on all variables and combinations thereof. My language is Power Basic, a full capability language with direct access to memory through pointers and completely structured like C. My operating system is Windows 11 on a powerful Sager gaming computer. I have used my edge painting algorithms to invent and patent a new way to upsize my images so I can produce high quality art at 300 dpi up to 100 inches by 100 inches.

Which scientists and/or artists inspire and/or have influenced you? I love several of the early pioneers of modern art. My favorite is Monet, and I am also very fond of Mondrian, Kandinsky, Picasso, Klee, Klimt, Renoir, Van Gogh and Miro to name just a few. But my late brother Gene is by far my greatest artistic influence. In the sciences, Einstein has been a lifelong hero. Generally, great scientists like Newton and Feynman have been a strong influence. More personally, my first significant influence was my uncle Joe Ballam, the man who married my father's sister Ethel. He became a distinguished physicist, for 17 years the first director of research on the Stanford Linear Accelerator. A small anecdote illustrates this. By the time I was 4 my family knew I was precocious and science oriented. At that time Joe was a post-doc in cosmic ray physics in a lab at the north end of the Princeton University Quad. One day Aunt Ethel decided to take me on a visit to the lab. As we approached the steps at the entrance, she suddenly grabbed my shoulders and turned me 90° right. In the distance an old man in a long coat was slowly ascending some steps. My aunt said "That's Albert Einstein". A simple memory but still clear in my mind. The next major influence was the close family friend Lou Zeitz, a biophysicist who spent many years leading a lab at Sloan Kettering. Besides being a fine scientist, he was an extraordinarily kind man. Remarkably, I did not bond with any of the large number of leading scientists at Caltech, despite working every summer in the labs. My next major influence is Professor Arthur Karlin of Columbia University, a member of the National Academy Of Sciences. I was and remain his only grad student, in neurophysiology. I left a fine project in his lab for personal reasons having nothing to do with him, but his insistence that I believe in myself has helped me persevere in science. After resuming graduate school at UMCP and a few years of searching in Maryland I stumbled into Harry Meryman's famous blood lab at the American Red Cross. There I partnered with Robert J. Williams, a polymathic biologist, to investigate the biophysics of deep freezing resistance in trees (my PhD) and a little later I worked extensively with Tsuneo Takahashi and Bob Williams on the biophysics of the cryopreservation of blood cells. Starting in 1992 I began work on protein stability with a Bulgarian scientist, Latchezar Tsonev. We have worked closely together to the present on proteins, deep freezing resistance in certain subtropical plants, and the invention and marketing of the first wide ranging pH gradient technology in chromatography