Fractal Art and Design

Fractal Gallery

This is a selection of finished, single-edition prints. All prints are on high-quality archival photo paper. These prints are one-of-a-kind and are for sale. To preserve their value, I do not provide the parameters, and will never reprint. Please inquire through the contact button, above.

I have recoded my gallery to utilize a more traditional “tiled” layout. Just click on a tile to view an enlargement. If it doesn't seem to be working, refresh your page with Ctrl-F5.

Stage II

After spending some time exploring and developing my fractal application and my style, I feel that these works have achieved a new artistic level above my initial exploratory works.

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  • Flight
  • 6/16/2019
  • 20" x 20"
  • Photo Print
  • Single
  • $985
  • There are multiple methods to depict a fractal rendering. This one uses angular cycle counting to measure how rapidly each point changes. The result was unexpected. This is a fairly deep zoom into the Negabrot (exponent of -2) using this technique. There is a lot of energy in this image.
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  • Order
  • 4/20/2019
  • 20" x 20"
  • Photo Print
  • Single
  • $985
  • An orderly progression of chromed surfaces resulting from a mild zoom into the multibrot set at a fractional exponent below 2 with an Exponential function applied produces a fairly imposing image. It is somewhat... Orwellian... I attempt to title my pieces with words that reflect not only what appears to be there, but how they feel.
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  • Synergy
  • 4/10/2019
  • 20" x 20"
  • Photo Print
  • Single
  • $985
  • Inserting trigonometric functions into the periodic negative exponent Multibrot space results in smooth, curvilinear lines in complex patterns. Rendered in greyscale, it looks like the curves are holding in the energy of this image.

Stage I

These are works from what I would consider an exploratory stage, where I was building my fractal application and exploring what is possible. This is not to say that exploration has ceased, just that I feel that my work is starting to mature beyond this stage.

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  • Amphibian
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • This is a vertical “slice” rotated an odd 70-degree angle through Multibrot space, positioned just below the traditional Mandelbrot set. Is it a school of fish, or a lounge of lizards? I had to look up what a group of lizards was called. It reminds me of Escher's “Reptile” tiled etchings, and his choice of subject has multiple levels, rep tile. This fractal's complexity renders countless creatures.
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  • Aquifer
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • This is a vertical slice of the multibrot set, just below an exponent of -1. This area tends to be very fragmented, and looks like water embedded in rock.
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  • Arachnoid
  • 01/06/2019
  • 12" x 12"
  • Photo Print
  • Single
  • $300
  • I found this spidery image in a “vertical slice” through multibrot space at an exponent of around 119. Things get very squished up here, so this had to be stretched 4,000% horizontally to see the image. The fractal is rendered with a complex color scheme with both escape-time and periodic rendering through some trig functions to enhance its leggy details (whew).
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  • Bamboo Forest
  • 10/21/2017
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • This leafy image is a moderate zoom in a vertical slice of the negative space under the multibrot set, with an exponent between -1 and -2. It is rendered with periodic rendering, complicated by the extra iterations required for the smoothing algorithm. The leafy, twiggy result reminds me of bamboo.
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  • Bluebird
  • 2/20/2017
  • 12" x 8"
  • Photo Print
  • Single
  • Sold
  • A flutter of wings and feathers appears just underneath the traditional Mandelbrot set in the Multibrot space. The exponent is rendered vertically in this “Multibrot Slice” at a 70-degree angle from the real axis. “Bluebird” won “Special Recognition” in the Light, Space, and Time Gallery 2017 “Abstracts” exhibition.
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  • Braided
  • 3/20/2015
  • 12" x 18"
  • Photo Print
  • Single
  • $545
  • The twisting threads, colors, and textures in this traditional Mandelbrot magnification remind me of a braided rug. The color ramps use prime numbers to limit repetition, increasing the color depth of the resulting fractal.
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  • Chains
  • 11/29/2014
  • 18" x 12"
  • Photo Print
  • Single
  • $545
  • This is my very first finished piece. It is a deep magnification into the Mandelbrot set, with a large escape depth setting and the beginnings of simplified Lyapunov periodic mapping to produce the gentle, smooth gradients.
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  • Champagne
  • 11/29/2016
  • 1:3 to be printed
  • Photo Print
  • Single
  • $745 (at 12x36)
  • A “Multbrot” is a variation of the Mandelbrot set rendered with an exponent other than the traditional “2.” This is a magnification of the set with a high exponent of 71. Why 71? Why not? The swirling, bubbly texture lends to its name. “Champagne” won “Special Merit” in the Light, Space, and Time Gallery 2017 ”Abstracts“ exhibition.
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  • Clematis
  • 2/16/2017
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • You're “not supposed to” render a negabrot with escape-time mapping. It's “wrong.” That said, this is a negabrot (a Mandelbrot set with an exponent of -2) rendered with a combination of escape-time mapping and simplified Lyapunov periodic mapping. In other words, it's a “hybrid,” like a lot of plants you can find in a garden. This image reminds me of its namesake, a climbing, flowering vine.
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  • Coriolis (Sold)
  • 5/24/2015
  • 3" x 3" cube
  • Photo Print Cube
  • Single
  • Sold
  • Here is a deep zoom into the Mandelbrot set. The actual image was renderes into six squares and mounted on the sides of a cube. The colorful swirls seem to wrap around the edges.
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  • Dragon Scales (Sold)
  • 9/1/2016
  • 8" x 12"
  • Photo Print
  • Single
  • Sold
  • The scaly texture comes from a deep magnification of the Mandelbrot set. I selected colors reminiscent of traditional Chinese art. “Dragon Scales” won “Special Merit” in the Light, Space, and Time Gallery 2016 “Open” exhibition.
• • 
  • An Evening in the Garden
  • 06/30/2017
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • This is a moderate zoom into a sinewave variation of the Mandelbrot set. Traditional escape-time mapping renders it as “snow,” but period-mapping reveals a whole different picture. Careful adjustment of the color parameters produces an organic, yet otherworldly feel.
• • 
  • Equinox
  • 12/20/2016
  • 3:1 to be printed
  • Photo Print
  • Single
  • $745
  • Swirls of winter snow, crunchy autumn leaves, and hot summer breezes are all reflected in this long slice of the Multibrot set with the exponent rendered vertically just below -1. Simplified Lyapunov periodic mapping (whew) reveals intricate details in this area.
• • 
  • Fern Garden
  • 06/15/2018
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • This is a sinewave variation of the Mandelbrot set with both escape and periodic rendering applied. Overlaying these techniques brings out the periodic nature of the sine function with the enhanced detail of the escape function.
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  • Fluidity
  • 10/24/2016
  • 3½" x 3½" cube
  • Photo Print Cube
  • Single
  • $145
  • This deep magnification of the Mandelbrot set uses complex color ramps to highlight oily, swirly forms. The limits of the ramps form broad, curving edges, creating overlapping fluid shapes. This is just one of six renders of this space, each mounted in the side of a transparent cube.
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  • Fragments of Imagination
  • 06/15/2018
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • What is it? It could be a broken stained-glass window, an abstract bushy tree... Setting the exponent to a fractional value, in this case around 5.6, produces fragmented patterns.
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  • Glass #2
  • 10/28/2017
  • 10" x 10"
  • Photo Print
  • Single
  • $245
  • The trig functions normally tend to produce a random mess when applied to the Mandelbrot formulas. However, since trigonometric functions are basically periodic in nature, applying periodic mapping can draw out hidden patterns. Using an arctangent variant of the Mandelbrot set with period mapping applied, a glassy, transparent image emerges.
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  • Ice (Sold)
  • 3/14/2015
  • 12" x 18"
  • Photo Print
  • Single
  • Sold
  • I was challenged to re-map “Magma” to create a frozen, icy effect to contrast the deep, hot look of the original work. This is the same fractal, with a completely different effect.
• • 
  • Incursion
  • 3/15/2015
  • 12" x 18"
  • Photo Print
  • Single
  • $545
  • This is a magnification of the traditional Mandelbrot set with a tightly-repeating grayscale color map applied, resulting in a highly-energetic pattern.
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  • Longing
  • 4/10/2019
  • 12" x 12"
  • Photo Print
  • Single
  • $300
  • Applying trig functions to the complex conjugate of the Julia at a fractional exponent, I discovered this fuzzy figure peering back out at me.
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  • Magma
  • 3/20/2015
  • 10" x 20"
  • Photo Print on Metal
  • Single
  • $545
  • This is a deep magnification into the Mandelbrot set. The various cracks and veins inspired me to give it a hot, dark, deep-earth look. I added the “interference” capability to my fractal application just for this particular work to increase the available complexity of the color map.
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  • Melted
  • 06/15/2018
  • 12" x 12"
  • Photo Print
  • Single
  • $345
  • This is from the sinewave variant of the set. I just love the glassy, transparent textures that come out in this application.
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  • Outburst (Sold)
  • 11/20/2018
  • 12" x 12"
  • Photo Print
  • Single
  • Sold
  • This is a detail of the tower of powers fractal. I have applied a complex gradient to enhance subtle changes that occur within the “fronds” of this fractal. As you zoom in, the interaction of these curves becomes more interesting.
• • 
  • Periwinkle
  • 2/16/2017
  • 8" x 12"
  • Photo Print
  • Single
  • $245
  • Here is a moderate zoom into the bottom-right area of the Mandelbrot set. I was experimenting with techniques to render inside the set. The resulting curving forms produce an iridescence and depth beneath the complex, branching shapes.
• • 
  • Ripples
  • 4/6/2017
  • 8" x 12"
  • Photo Print
  • Single
  • $245
  • A variant of the Mandelbrot set takes the absolute value of the formula on each iteration. The result is very different. This is a deep magnification of the “Burning Ship” fractal. It looks like you are looking upward through rippling water at an old cityscape. This fractal tends to be noisy, so rendering required 16X supersampling to smooth it out.
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  • Shoreline
  • 06/15/2018
  • 12" x 12"
  • Photo Print
  • Single
  • $345
  • The burning ship variant of the Mandelbrot set uses the absolute value (positive value) of the formula, and produces a rather noisy, turbulent result. Applying periodic rendering to the inside of the set reveals some interesting patterns. This image is technically “inside” the set, but periodic rendering brings out some normally invisible activity.
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  • Starlight (Sold)
  • 5/24/2015
  • 3" x 3"
  • Photo Print Cube
  • Single
  • Sold
  • Millions of stars glow in tight clusters in this deep magnification of the Mandelbrot set. This fractal is split into six separate squares and mounted into a cube frame.
• • 
  • Storm Surge (Sold)
  • 5/23/2015
  • 3" x 3"
  • Photo Print Cube
  • Single
  • Sold
  • This is a more traditional rendering of the Mandelbrot set. There is a lot of energy in the swirling, branching forms. This is just one rendering of six in this space, mounted into a cube frame.
• • 
  • Striped Sky
  • 01/06/2019
  • 12" x 12"
  • Photo Print
  • Single
  • $300
  • This was found inside the “Burning Ship” fractal. Periodic rendering reveals a lot of interesting turbulence in here. Applying the Julia form in this area produces the repeating, reducing pattern.
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  • Sunrise
  • 3/13/2019
  • 12" x 12"
  • Photo Print
  • Single
  • $300
  • Studies find that the human brain prefers fractal repetition at a factor of about 1.4. So I tried it. This sunny pattern is a Julia variant at that exponent. Period-rendering brings out the warm fire in the middle.
• • 
  • Sunset on Ice
  • 12/17/2016
  • 14" x 11"
  • Photo Print
  • Single
  • $345
  • The fractured nature of this rendering comes from the very turbulent space between -1 and -2 in the Multibrot set. The exponent is rendered on the vertical axis, with simplified Average-vector periodicity mapping to bring out the textures. This pattern reminds me of ice crystals that form overnight on the road, so I added a hint of morning sun.