QS Image Gallery

These original images by Michael Sargent were rendered using my own software and the Persistence of Vision ray tracer, with post-processing by Adobe PhotoShop and MetaCreations Painter. They exist as 16.7-million-color JPEG's. Please set your browser and/or image viewer to utilize a true color graphics mode, or you won't see these pictures in their full glory. Click on the thumbnail icons to see the full-sized images.
Although I tend to write my own fractal-generating programs, Fractint is the sine qua non for anyone interested in studying fractals and generating them on a PC. Fractint is available at many Internet locations, including Noel Giffin's outstanding fractal archive called Spanky, and the UTK Math Archives. It also accompanies the invaluable reference Fractal Creations. This book and the definitive POV references, Ray Tracing Creations and Ray Tracing Worlds, are published by the Waite Group Press.

Can computer graphics be art? For what it's worth, here's my opinion on this burning question.
This is a fractal height field utilizing two regions of the Mandelbrot set, generated as "continuous potential" images by Fractint. Every picture needs a light source, and this one uses a Hubble Space Telescope photograph of the star Eta Carinae. 640 x 480 pixels
Everyone who does ray tracings is obligated to make at least one Utah Teapot. Here is a version with a textured foreground for reflection and a photographic background. 640 x 480 pixels
A standard Julia image was rendered with a gold and silver palette, using an orbit-trapping coloring formula. Then it was used as a height field to simulate a three-dimensional piece of fractal jewelry. 800 x 600 pixels
This attempt to render erythrocytes and lymphocytes started with a torus and Bezier patch. The patch was fine-tuned with a modelling interface for POV called Moray. 640 x 480 pixels
This picture is a study in refraction. The base is a Mandelbrot set. Inside the set is a Perturbated Gingerbread Man fractal, based on formulae developed by Fausto Barbuto and Victor Ielo. 640 x 480 pixels
The tiling pattern for this image was generated online at the University of Minnesota Geometry Center's interactive Web site. A 2-dimensional image of the pattern was then applied to a spherical surface with POV. 640 x 480 pixels
Here are some images utilizing fractals generated with standard escape-time algorithms. The Volterra-Lotka and "Escher Julia" formulae from my QS W95 Fractals program have been incorporated into Fractint. Other classic formulae, including the magnetism models, have been there all along. I've not seen the enhanced sine formula in other fractal software.
Here is a 24-bit zoom into the Mandelbrot set, which seemed to make a perfect frame for Waterhouse's portrait of Psyche. 480 x 480 pixels
This image is a manipulation of a zoom into the Mandelbrot set. 640 x 460 pixels
One of my favorite fractals from Peitgen and Richter's The Beauty of Fractals is derived from the Volterra-Lotka predator/prey formula. Here is an image from this formula, applied to a sphere. 640 x 480 pixels
This is a zoom into a Volterra-Lotka image in 24-bit color. 640 x 450 pixels
This image is composed of "tile Julia" or "Escher Julia" fractals. These circular curiosities were introduced in The Science of Fractal Images. Peitgen and Saupe saw an analogy between these fractals and Escher's Circle Limit series, in which characteristic interlocking figures recede toward an infinity that, paradoxically, is bounded by a finite circle. The formula of these fractals is a variation on the standard Julia theme. The target set, rather than being the usual disk around infinity, whose diameter is defined by a "maxsize" variable, is a second, scaled, Julia set:
     T = z: | (z * factor)^2 + c | < maxsize
1024 x 768 pixels
This eclipse-like image is an inverted tile Julia fractal. The font of the inscription is from "Thror's Map" in The Hobbit. The inscription itself reads, "All the gods are one god." The concept is attributed, in a work of fiction, to the Druids. I don't claim the expertise to verify that, but such an open-minded perspective seems quite unique to any formal religion. 640 x 480 pixels
One also can find "enhanced sine" images similar to this one in The Science of Fractal Images. 800 x 600 pixels
This image is a straightforward inversion of the preceding one. 800 x 600 pixels
This fractal was generated from one of the magnetism formulae explored in The Beauty of Fractals. The large inside region was colored using only a 256-color palette, with no true color algorithms. This demonstrates that palette-based graphics modes can produce gradients which are almost as subtle as those in true color modes. They just can't be as extensive. 800 x 600 pixels
The following images were made with my QS Flame program. They are blends of chaotic attractors produced with formulae created by Scott Draves.
This moth-like flame image seemed most at home fluttering over a moonlit landscape. 800 x 600 pixels
This image owes its rather stark detail to the use of a small filter radius and a large oversampling factor. 800 x 600 pixels
This image uses the same parameter set as the previous one, with a rather large filter radius. 800 x 600 pixels
This image was done by my friend Jeff Field, using overlays of multiple parameter sets. 640 x 480 pixels
Here is another QSFlame image, using a parameter set from my friend Fausto Barbuto. 800 x 600 pixels
In his fanciful book Chaos in Wonderland, Cliff Pickover describes creatures on Jupiter's moon Ganymede who visualize beautiful chaotic attractors in their dreams.
Here is an image of one such fractal dream. 800 x 600 pixels
Here is another fractal dream image generated from one of the formulae in Chaos in Wonderland. 800 x 600 pixels
As the title implies, the images in Symmetry in Chaos by Field and Golubitsky are chaotic attractors which display astonishing degrees of symmetry. The following images were made with my SymXaos program.
This image was generated from one of the "symmetric icon" formulae described in the book. 800 x 600 pixels
There also are two "quilt" formulae in Symmetry in Chaos. These produce square and hexagonal patterns with "seamless" borders, so that they may be combined by tiling to cover large areas. This image shows a complex interrelationship among several repeating patterns. 640 x 480 pixels
The following images were made with my Line Integral Convolution filter program.
This is a rendering of a floral photograph. The left half of the image was done using a Gaussian blur of the photograph as a source of the vector field. The stream lines of the original image are seen easily. The right half was done using a Gaussian blur of white noise, with the ramp filter option. This approach yields a different painterly effect. 760 x 510 pixels
Here is another floral LIC image. 540 x 600 pixels
Landscapes often respond well to LIC techniques. Perhaps part of VanGogh's eccentric genius was the ability to visualize vector fields directly in nature. 800 x 555 pixels
Here is another LIC landscape. 800 x 500 pixels
Can computer graphics be art?

This question has been addressed since the earliest groundbreaking publications by Mandelbrot and Peitgen's group. Here is a summary of my perspective on this issue:
When we understand a mathematical truth (whether it is represented by an equation, a graph, a fractal image, or just an idea), it can seem beautiful, as John Keats suggested. However, such "beautiful truth" is not art, but only a preliminary step. Mathematics is both a tool and a source of inspiration. But that is not enough for art, any more than a sunset, or a crystal, or a flower.
Impressive pictures of fractals, even when they appear in such wonderful books as The Beauty of Fractals, or when they appear on the Web enhanced by clever true color algorithms, are not necessarily art. But look at some of the pictures in The Beauty of Fractals, where fractal images are manipulated in three dimensions, or used as height fields to create landscapes of fantasy. Those pictures do qualify as art, because they start with a concept in the human imagination, and then "artifice" is employed to cause that concept to become visible. Such artifice includes time-honored processes such as creating forms, composition, lighting and meticulous selection of color palettes. Whether the artist uses a brush to apply paint on canvas, or mathematical software to produce glowing pixels on a monitor, it is this human creative process which can use any source of inspiration, including mathematics, as a starting point for producing real art. Of course, there is nothing which prevents real art from being obscure, offensive, downright ugly, or otherwise of questionable aesthetic merit in at least someone's opinion.
With all the excellent fractal software available today, you can click on menu items to select parameters at random and magically, something beautiful arises from nothing. But that something is not art. There is nothing wrong with non-artistic digital images, just as there is nothing wrong with a beautiful sunset. But I believe that true art implies the deliberate creation of something unique and personal, something which is born of the imagination. A computer can never be programmed to generate art by itself. The human element of creativity is necessary.
Having made these assertions, I offer the conclusion of Herbert Franke's essay in The Beauty of Fractals: "The art of every age has used the means of its time to give form to artistic innovation.... Why shouldn't the computer, that universal medium of information and communication which has even invaded our private homes, be used as an instrument and medium of art?"

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