Gary Allen Smith

Explorations of a Virtual Geography

By Gary Allen Smith
1994, All Rights Reserved

Fractals are vast geographies existing as virtual universes calculated inside the computer. Different equations produce differently shaped virtual geographies. The Mandelbrot equation, first investigated by Benoit Mandelbrot, when plotted, produces the oddly balloon-shaped sea shown here.

The Mandelbrot Fractal (monochrome)

The shore of this sea is richly packed with grand vistas of complexity containing tendril-like structures, long sinewy rifts, giant sprays of fire and electricity, vast plains of color and lace, and even strange, alien organisms. From within this complex shoreline, I create my imagery.

The Mandelbrot shoreline is infinite. Mathematically, it can be expanded forever, but in reality is limited to the computing precision of the software used to generate it. The software I use can expand the Mandelbrot fractal to an image that is one-quarter of a light-year wide. At the same scale, 805 copies of our 7.3 billion mile diameter solar system would easily fit side by side across the image shown above.

The Structure of Fractal Art

Fractals are a unique form of image based on the rendering of non-linear algebraic equations. They require a computer to generate and can be painted in extremely bright and complex colors. They are very convoluted images that can be expanded infinitely and still retain a similar level of complexity. They have a structure that is mind-boggling and confusing.

Fractals appear to fold in on themselves, possessing a structure that hovers between two-dimensional drawings and three-dimensional sculptures. Looking at the two images Chrysolite Swirl and Chrysolite Ballet, one can see this paradoxical structure.

Chrysolite Swirl

On close inspection, one sees that Chrysolite Swirl is really an enlargement of the center area of Chrysolite Ballet. Yet, if one studies the myriad, feathery spines that outline the great swirling arms of Chrysolite Swirl, one realizes that they are miniature versions of Chrysolite Ballet.

Which came first: the swirl or the ballet? Where does one fractal end and the next one begin?

Chrysolite Ballet

The Technology of Fractal Art

The virtual nature of fractals causes many problems for the computer artist. Producing gallery quality images requires state-of-the-art equipment. The extremely high resolution needed to show the incredible detail in fractals demands a large amount of computing power. Beryline Lamina is composed of 22,325,625 pixels, many of which took several thousand iterations to compute. Calculating it required 88 hours of continuous computation on my 50MZ 68030 Macintosh with 50MZ FPU. Only very low-resolution version of Beryline Lamina is show here.

Beryline Lamina

I use dye sublimation and Iris inkjet technology to realize my prints. In dye sublimation, an emulsion contains dye crystals for each of the CYMK color separations. At each point, these crystals rupture in proportion to the desired color's components. The dyes leak out and sublimate together to produce the precise color.

Similarly, Iris inkjet technology mixes wet inks at extremely fine resolutions. Both technologies produce continuous tone images that do not exhibit the dot patterns of lithography. When magnified, my images show only smooth expanses of color.

The Colors of Fractal Art

In the computer, fractal images are stored as numbers laid out in a rectangular pattern. These numbers map to colors, producing the fractal image and making it visible.

By judiciously choosing the colors in a palette, I can affect the appearance of the fractal. The color palettes act as filters through which I view my fractals. Different color schemes accentuate different attributes of a particular fractal. A color palette that has smooth changes in hue while maintaining a constant brightness accentuates high complexity areas as in Chrysolite Swirl and Chrysolite Ballet. Colors arranged in bands of different hues that have deepening shades of the same hue within each band, accentuate low complexity areas as in Beryline Lamina and Embryonic Calculations.

Embryonic Calculations

Cryonic Tubulation is an example of a special, linearly increasing color palette. The colors are arranged in bands in the same way as in the low complexity palette described above, however, each successive band is wider than the previous one. This color palette produces a uniquely dominating shape containing a subtler complexity.

Cryonic Tubulation

Gary Allen Smith is a computer artist / software developer living in the San Diego area. He has spent the last 2 1/2 years exploring the Mandelbrot Fractal, documenting it through fine art. Gary is continually amazed by the infinite complexity of the Mandelbrot, and the viewer is reminded that the works seen here represent only a tiny fraction of his work. The above paragraphs are excerpts from his recent Explorations of a Virtual Geography installation at CyberFest '94. A book further illustrating his efforts is planned for release in late 1995.

Due to the inherent limitations of computer technology, the images included in this and other files included on this CD are faint reflections of the grandeur possible using state-of-the-art printing technologies. For more information and a color catalog send $4 to Gary Allen Smith, P.O. Box 891, Poway, CA 92074 or E-mail to "GaryAllen" on America On-Line.