In lieu of an abstract, here is a brief excerpt of the content:

Reviewed by:
  • BitArt
  • Luisa Paraguai Donati
BitArt Web site: <>. Artist: Robert J. Krawczyk

My first impression of BitArt led me to rethink the conceptual threshold between a piece of mathematical art and a mathematical, scientific graphic, both of which intend to create "a tangible experience" of abstract mathematical objects and concepts. This interdisciplinary interface is not a contemporary occurrence but has generated distinct aesthetic outcomes: artists are moved by poetic proposals that contrast with mathematicians and their accurate representations. Currently, the use of computers to produce these kinds of images has generated more systematic works, resulting in aesthetic experiences such as [End Page 83] simulation and visualization through the manipulation of algorithms and programming languages. This use of algorithms can produce a disintegration of symmetry, generating other relations and constructions in the organization of artistic works. In the same way, random options introduce the possibility of instability and unpredictability, breaking the systematic and symmetrical elements by embodying "something accidental"—a recurrent artistic procedure.

The BitArt site formalizes artist Robert J. Krawczyk's intention by researching mathematical concepts aesthetically in spirolaterals and a series of related strange attractor equations. In both situations Krawczyk investigates the possibilities of graphical visualization by describing and manipulating those expressions. In the "Art of Spiro-laterals" section, there is a gallery showing a variety of spirolaterals and a demonstration version. In another section, users can create their own spirolaterals by changing the parameters (turning angles, varying the number of turns or repetitions, and reversing all the turns) so as to visualize all the reversals without any prior knowledge. According to Krawczyk, "Spirolaterals were first encountered while investigating space curves and fractals in Abelson. What was intriguing about them was the simple procedure to generate them and the great variety that could result from modifying a small set of parameters." From the experience of investigating the rules of spirolateral generation, he obtained unexpected designs as results; this unpredictability, under controlled conditions, is what makes spirolaterals of continuing interest to him. The action of compounding forms and structures by changing parameters and using a variety of line thicknesses has generated infinite possibilities of rhythm, spatial directions and spatialities, and it characterizes the author's aesthetic interest.

In the "Dimension of Time in Strange Attractors" section, Krawczyk explores non-random equations of chaotic processes, to generate "spatial forms" that can be visualized and rendered when the element of time is introduced into their interpretation. By using coloring algorithms, he exposes the time element of the computational process that produces images of coherent 3D forms. Consequently, these images can be visually explained by a continuous movement of folding and unfolding their structure—endless bending and twisting.

Some contemporary artists are also involved in "the action of doing something" by working and playing with numbers in order to obtain and visualize forms, curves and spaces. According to Tania Fraga, "[these] artists have potentialised the environment using this 'something' as sign, as symbol, in experiences of presenting and not representing." As a result, these visual poetics can be understood as a space of possibilities which will be realized (actualized) in a certain moment, as something that "presents the virtual giving visibility and therefore reality." From the relation between users and graphical presentations, different unities can be revealed—hidden compositions not apparent from the theoretical description are disclosed by the visualization. This confirms Merleau Ponty's claim that "art is an operation of the expression— a phenomenon of the expression," that works in the "domain of the possible" to evoke experiences that will compose viewers' consciousness.

This is a valiant and engaging project but ultimately it is a slight disappointment. Thinking about the web site as a design, I find a visual and aesthetic difference between its intention and its content. Personally, I would have liked to see some elements from those curves and forms embodied in the site design so as to integrate its aesthetic context with Krawczyk's works.

Luisa Paraguai Donati
Department of Multimedia, Institute of Arts, Unicamp, Brazil. E-mail: <>


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pp. 83-84
Launched on MUSE
Open Access
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