The artist provided the following comments:

Two thousand years ago, Seneca wrote that "All art is but imitation of nature." Assuming this, if nature can be described mathematically, the same should be true of art. Of course, current-day mathematics is not sufficient to describe truly complex systems, like humans and their relationships, which are the subjects of much great art. And perhaps some of these areas will forever stay outside the realm of mathematical analysis.

Often abstract art, including music, is closer to mathematics. Those aspects of nature, like optimization problems, that are most easily described in mathematical terms often lead to an abstract beauty. Henry James wrote that "in art economy is always beauty".

Like most research mathematicians, I find abstract beauty in the elegant and economical structure of mathematical proofs, and I feel that this elegance is discovered, not invented, by humans. I am fortunate, however, that my own work in optimal geometry leads directly to visually appealing shapes, which can present a kind of beauty more accessible to the general public.

Mathematics can be related to art in many ways. One can study art mathematically, looking for symmetries or other relations in the construction of a painting or sculpture. Conversely, mathematical algorithms can be used to help create art: fractal systems, for instance, can recreate realistic shapes of plants, mountains and clouds.

Above all Fractal Art is an experimental art form. The artist is never fully certain what effect variables will have on the image. This fact connects, rather than separates, the digital fractal artist with the traditional paint artists. The chaos that occurs when a painter touches the canvas with the brush can never be fully controlled. Indeed, most accepted masters of the painterly arts find methods to guide this fractal force, as a horseman can never possess the power of the horse but only direct it to some degree. When working with only a fractal program, with no other graphic manipulation used, the image dictates to the artist what direction to proceed, and not vice versa, as with traditional drawing or painting techniques. The dedicated fractal artist spends hours making small changes to various parameters, looking for just the right effect or color scheme.

Artist begins with a blank "canvas", and creates an image, bringing together the same basic elements of color, composition, balance, etc., used by the traditional visual artist. Requiring of input, effort, and intelligence. The Fractal Artist must direct the assembly of the calculation formulas, mappings, coloring schemes, palettes, and their requisite parameters. Each and every element can and will be tweaked, adjusted, aligned, and re-tweaked in the effort to find the right combination. The freedom to manipulate all these facets of a fractal image brings with it the obligation to understand their use and their effects. This understanding requires intelligence and thoughtfulness from the Artist.

The final fractal image must be created, just as the photograph or the painting. It can be created as a representational work, and abstraction of the basic fractal form, or as a non-representational piece.

Dynamic painting is a movement in visual arts where paintings are updated on an on-going basis. The artist determines the general principles for image genesis and develops algorithms for transformation methods. The resulting image depends on a myriad of factors, and is, as a rule, unpredictable.

The Dynamic Paintings can be considered a generative art?an art that has been generated algorithmically by a computer system. Unlike all other generative art examples that account for just a few basic artistic principles and require very little artist input, Dynamic Paintings require skill of an artist. An artist begins creation of a Dynamic Painting by conceiving an idea for the painting, selecting basic colors, shapes and principles of their development over time. Unlike a conventional painter, the artist has to think in one more dimension to properly design the evolution of images as the painting would develop. Using various techniques that have deep roots in the styles of conventional paintings, an artist converts the brush strokes into algorithms that can precisely convey his original design of a digital painting. Once the Dynamic Painting has been designed and programmed, it is up to a computer system to bring it to life.

This algorithm represents the "DNA" of the picture. Just like the DNA of a living organism, with a slight mutation, the image algorithm can produce an infinite number of unique paintings. A carefully devised "mutation" algorithm uses a computer to generate a series of distinct images that follow the style and concept of the original painting. This "mutation" process can be slowly animated over time to produce a fluid motion within the element of a painting; producing a never-ending and never repeating show. The painting is always in the state of a perpetual transformation. The picture living its own life with objects moving and transforming but still following the original artist's concept.

Sahaj Patel's art on the Web