The Art of Robert F. Kauffmann

Robert F. Kauffmann is an award-winning artist, writer, and computer programmer from Cinnaminson, New Jersey. While still in college, Mr. Kauffmann developed his own artistic style, inspired by his background in computer science and mathematics as well as the work of the mathematician B. Mandelbrot, inventor of fractal geometry, and the graphic artist M. C. Escher. His designs portray visual paradox using mathematical structures as expressive tools. He calls this style Mathematical Surrealism.

Mr. Kauffmann's graphic artwork has been featured in numerous shows in Philadelphia, Chicago, New York City, Miami, and other venues nationwide. His work has also won a number of awards and been published in various periodicals.

Now for the first time, a selection of his most extraordinary works are available as limited edition posters. Available exclusively from Arx Publishing, these beautiful reproductions are suitable for framing, yet priced reasonably enough to be accessible to everyone.

*Please note that images appear on this web site at a considerably lower resolution than the actual artwork.

Dragon Limit I
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The Dragon Limit series takes Escher's idea of approaching limits to infinity and generalizes it to include the tiling of fractal figures which approach a bounding limit which is also fractal. The fractal in this case is based on constructions by Mandelbrot of a figure called a "Twin Dragon" which he showed could be subdivided in order to tile a plane. The Dragon Limit series consists of four variations arising from two different coloring schemes and two different methods of dividing the space.

In this first example from the Dragon Limit series, design, the dragon-tile approaches the border limit without ever actually touching it. This can be seen as an illustration of Xeno's paradox. This also illustrates the concept of "open sets" in set theory, which specifies an area on a plane minus its border. (think of a solid object with its skin removed.) The exact definition of an open set is actually somewhat less intuitive. It is any set in which all of its points are a non-zero "distance" from any point outside the set.

Dragon Limit II
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This design is like Dragon Limit I, but using a darker coloring  scheme.

Dragon Limit III
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In this design, the dragon-tile approaches the border limit, growing smaller with each iteration. Unlike Dragon Limits I & II, each tile touches the border limit in exactly two or three places. All of the tiles together presumably fill out the entire length of the border limit. Thus, the tiling scheme illustrates the concept of "closed sets" in set theory, which specifies an area on a plane which has a border. (Points which are zero-distance from points outside the set.)

Dragon Limit IV
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This design is like Dragon Limit III, but using a darker coloring scheme.

Magic Castle
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This design is based on the "impossible perspective" prints by M.C. Escher (BELVEDERE, WATERFALL, ASCENDING AND DESCENDING). The design takes advantage of the loss of information inherent in a projection of 3D space to 2D space to create the optical illusion of a 3D structure which seems to recede into more than one direction at a time. Roger Penrose stated that such structures were impossible in three dimensions--implying that such might be possible in higher dimensions. Penrose and his father were the first to experiment with "impossible perspectives."

Magnetically Distorted
City
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Winner of the Benton Spruance Memorial Award for Prints, 1999

Moth
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Sunflower
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Octagon Limit
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Celtic Dragon
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A dragon's image in a spiral is built from interlocking spiral S-curves which are, in turn, inscribed with dragons made of the same. The smaller dragons provide a delicate interlocked pattern which is reminiscent of Celtic design.

Medium: Serigraph ~ Original Dimensions: 24"x18"
© 1999 Robert Kauffmann.  All Rights Reserved.

Division of Plane
with Dragon
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This piece started as an exercise in topology, the question being, "Can an interesting composition be created by drawing a single continuous line?" The eventual result was a single sinuous curve dividing a plane into two halves-(red and white) which defines the image of a coiled dragon striking. A side-effect of this design is that the difference between figure and ground becomes irreconcilably ambiguous.

Medium: Serigraph ~ Original Dimensions: 18"x24"
© 1990 Robert Kauffmann.  All Rights Reserved.

L Dragon
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This design is a filled-in version of CLOSED CURVE WITH DRAGON (not shown on this page). It started out as an earlier version of DIVISION OF PLANE WITH DRAGON (above), depicting an L-shaped dragon. The curve in the original was closed, instead of open-ended.

Medium: Serigraph ~ Original Dimensions: 18"x24"
© 1993 Robert Kauffmann.  All Rights Reserved.

Holographic Dragon
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This carries the design of KIDNEYBEAN DRAGON (not shown here) to infinite recursion. It is called 'holographic' because, like a holographic plate, when divided, each fractional piece contains a complete but less resolved copy of the whole.

Medium: Serigraph ~ Original Dimensions: 18"x24"
© 1992 Robert Kauffmann.  All Rights Reserved.

Holographic Seahorse
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Bifurcating Fish
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Turtle & Shell
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Android Face
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Bach with Fugue
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Beethoven with Turbulence
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Face with Turbulence
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Pear Tree
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Tree
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