Yoishiro Kawaguchi's Mutation (1992) and Cell: Artificial Life Metropolis (1993) differ from his early 3D computer art in their multifariously colored textures, their use of new malleable, liquid forms, and their folding, enveloping, mutating surfaces. Kawaguchi's recent animations appear to be reflections of Deleuze's reading (1993) of the mathematics of liquid folds, his study of infinite curvilinear forms. Kawaguchi's 3D animations move by algorithms that simulate fluid and elastic folding surfaces. Deleuze describes how the coherent parts of fluid and elastic 3D bodies form folds such that when they are continually divided to infinity in smaller and smaller pleats and compressions of time and space, they always maintain their cohesion. Reflecting on the geophilosophy of ripples, waves and the surface crests of turbulent water, Deleuze defines matter as having a porous, spongy or cavernous texture that can be surrounded and penetrated by increasingly vaporous flows and waves of fluid. Like Kawaguchi's liquid constructions, Deleuze suggests that the folds of natural geography, of water, winds and veins of metal ore, resemble the curves of conical forms that sometimes transfigure into hyperbolas or parabolas.

Mutation follows the metamorphosis of highly abstract objects that flow, fold and fragment into innumerable permutations. In Cell, Kawaguchi experiments with liquid architectures as he builds a fugitive, molten megopolis of artificial life. These 3D animations epitomize Kawaguchi's work during the 1990's. Regarding form, his art is also an expression of the hyperbolic geometry of curving surfaces and of a modulating, synthesizing, liquid architecture capable of representing elastic or deforming topological constructions in 3D cyberspace. Like Malevich's architectones, Kawaguchi's 3D animations extend formalism's concern with form, surface and texture to include the language of abstract topology and folding surfaces.

As if he has Kawaguchi's work in mind, Novak (1991) describes the unusual transformations in the liquid architecture of cyberspace as the artist or animator generates and varies objects in time. He perceives cyberspace as a modulating, artificial architectural space. Liquid, visionary architectures offer an excess of possibilities in shape, contour, texture and topological construction. Novak suggests that we can now draw a comparison between sculpture and computer constructions, because liquid architectures, like hybrid abstract sculptures, produce aesthetic beauty or sublimity, structure or lack of structure, weight or weightlessness, lavishness (expense) or economy, details or simplicity, uniqueness or universality.

Kawaguchi's Mutation (1992) is a liquid, morphing 3D meditation on the endless repetition of "biocosmic" ideas in action. Kawaguchi uses growth algorithms and elaborate, multilayered textures to visualize the fluidity of changing, artificial, biomorphic shapes and creatures that exist at the interstices of microbiology and computer code. He speaks to the collapsing boundaries between art and science. Mutation invokes visual impressions of conceptual art, geometric abstraction and pattern painting, but its spatial structures actually reflect the recursion, repetition and randomness of computer growth algorithms in operation. Kawaguchi's "growth model" is a dynamic, non-deterministic process that allows constructive mathematics to take its course; a recursive structure of simple rules within complexity.

The fluid, seemingly part-serpentine, part-liquid undulations of Mutation's artificial forms resemble the movement of sand on the ocean's floor, the simulation of wave motion or lava flow, or the ripple effects of water after an object's touch. The radiating, shimmering texture surfaces on the abstract objects are the composites of animated form, watery rippling surface, manifold color, reflection and refraction. The simulationist computer compositing and inflection of multilayered texture maps using ray tracing techniques in 3D animation embody the computer artist's concern with enfolded, planar or other elastic topological surfaces in 3D cyberspace; the seamless, modulating, liquid architecture of complex topological forms in digital realms.

Like tangible, plastic, but less durable kinds of digital architecture and construction, modernist artists of the past also invented entire worlds without explicit reference to explicit reality. For example, Malevich's architectones combine flat and curved surfaces with round and rectilinear forms in three dimensions and in ways that refuse symmetry. Curving non-Euclidean forms are combined with Euclidean geometric shapes and spatial forms (squares, cubic volumes and parallelograms) as to constitute the basis for a new vocabulary of visual signs. Each architectone is assembled from the artist's intuitive elements and not according to mathematical formulas, as was the case with the contemporary work of the De Stijl neoplastic movement. Mondrian, Malevich, Klee and Kandinsky thus prefigure or antecede folding, liquid architecture, but the similarities are sometimes astonishing. If we wonder, what would life be like inside a cubist universe or a Magritte trompe l’oeil, then we may find the answer inside Kawaguchi's Mutation.

In Cell: Artificial Life Metropolis (1993), Kawaguchi seems to take the idea of a folding, liquid architecture more literally as he constructs a transmogrifying metropolis of fluid skeletons and spines. He experiments with helixes and mini-spirals that form aggregates of slippery, metallic caverns, plateaus, and long columns of coils that snake like household electric wire around cyborgian structures. The observer is unsure whether she is journeying through a robotic body, or witnessing the cool blue tectonic plate movement of some alien geological forms. Like Haraway's cyborg figures (1985, 1997), Kawaguchi's artificial creatures are hybrids of machine and organism, techno-genetic bodies capable of "mating" by exchanging genetic and technical material so that new configurations can emerge within the virtual arena. These artificial figurations are important in delineating the ontological nature of virtual worlds as they pertain to topological representation and simulated visual forms. Following Eisenman (1993), the enveloping surfaces of The Cell also hold the potential for future cyberspace architectures derived from planar folds and 3D volumes.

In a similar way, the work of Uri Dotan, computer artist, in homage to 1960's painter Frank Stella, epitomizes the new synthetic possibilities of virtual space as the complex creative expression of expanded computer code in modeling, lighting, ray tracing and transparency. The complex geometry of curved abstract shapes elaborated in contrapuntal, curving, liquid 3D forms, and in combination with heavy texture mapping, draws attention to surfaces that both reflect and distort the virtual reality around them. Dotan's digital pieces appear to be the simulacra of the unseen, reminiscent but unlike objects in nature. Like Kawaguchi's biocosmic constructions, they belong to no "real" space but to hermetic, alternative worlds.

Returning to Kawaguchi's liquid figurations, his recent work did not appear overnight, but are the offspring of many years of tweaking and amplifying his growth model. His earliest animation work, Pollen (1975) and Lines (1976) duplicate the rotating movement of dotted lines and spirals reminiscent of Gabo's work in plastic fibers from the 1920s and 1930's. Shells (1976), a prototype of the auto-multiplying growth algorithm, animates the delicate, soft extrusion of hollow wire-frame conch shells, horns and cones. In Growth: Mysterious Galaxy (1983), Kawaguchi introduces some new organic structures, such as his embryonic dolphins of liquid space, his red and green metallic tendrils, and his pink undersea chorals. He elaborates the play between surface and liquid submersion in Ocean (1986) as tubular, twisted helixes wind around flourescent green undulating ocean floors. Ocean also cameos Kawaguchi's first use of ornate, reflective surface textures. Float (1987) follows the voyage of unknown, perfectly golden, multifaceted globules through luminous organic whirlpools.

As testament to Kawaguchi's widely-recognized, distinctive style, Festival (1991) features a marine carnival of sea urchins, choral, sea amoeba and other fractalized creatures. Surface textures are now so multifarious and fugitive that they transgress the boundaries of the sublime or indescribable. Kawaguchi's folding, liquid architecture is consequently a dematerialized, ethereal, modulating architecture that is not satisfied with space, form, light, weight, etc. in the physical, bodily world, but corresponds to the merging or diverging of abstract topological objects and elements in mind spaces.

Rewriting formalism: abstract form in hybrid new media

The formalists of the 1960's, Greenberg (1967), Fried (1995), Krauss (1968), and Rose (1967), also express some interest in how the 3D sculptural event in "real" Cartesian space creates spatial metaphors between objects. In "Sculpture in Our Time," Greenberg (1958) suggests that we permit sculpture greater latitude of figurative allusiveness than other media, because it remains tied to the third dimension. The illusion of organic substance or texture is analogous to 3D in pictorial perspective (such as that in 3D graphics or canvas arts) and, Greenberg continues, this illusionism, literalness, or conceptual content has become an advantage rather than a hindrance. Greenberg chooses the sculptures of Jules Olitski as an epitome of modernist abstraction, because they create the illusion of capturing and folding surfaces of color in 3D space, an effect that seems to render them weightless. Instead of the illusion of things, they offer us the illusion of modalities, namely that matter is incorporeal and weightless.

Greenberg emphasizes the radical abstractness, or unlikeness to nature of Olitski's work (a frequently used euphemism in the 1960's), and the "weightlessness" of his sculptures in the way he says that they resemble Alexander Calder's mobiles. "Weightlessness" is a term from abstract art that implies free movement and a sense of not being grounded. Weightlessness and modality are the basis of formalism's new illusionism where matter is weightless and corresponds to some non-Euclidean algebraic geometric space not unlike cyberspace. Again, this kind of weightlessness belongs to the tradition of non-monolithic sculpture that we derive from cubist collage and with a cerebral and not a physical understanding of 3D form. Some critics, such as Krauss (1968), carry the cubist metaphor of illusionism to extreme conclusions: optical illusion becomes tactile opticality, sensuous to touch, as Krauss pushes the micrological analysis of the grain of sculptural surfaces to inordinate refinements.

Picasso's cubism indulges in and extends non-Euclidean paradigms of rounded or curved spaces in discontinuous, fractured collages. While Poincaré wrote about the tactility of curved space, Picasso's cubism enabled the radical materialization of this new space. Mondrian points out that cubism brings art to the threshold of a break with nature: It loses its unity by expressing the fragmented character of the appearance of objects. The tragic in nature is manifest as corporeality, and this is expressed plastically as form and color, as curvature and the "capriciousness" and irregularity of surfaces. Similarly, Deleuze (1993) discusses the importance of the plastic fold by showing us that matter is folded twice, once under elastic forces (of water, wind, ore, or magma), and a second time under plastic, derivative, organic and machinic forces. Folding-unfolding can no longer be equated to tension-release, or contraction-dilation, but to enveloping-developing and involution evolution. The plastic organism is defined by its ability to fold and unfold its own parts, not to infinity, but to a degree of development inherent in its species. In the theory of non-Euclidean curving surfaces, Deleuze distinguishes elastic forces from plastic, "machinelike" forces that are present in modernist culture and artifice, including the curving, pleated color surfaces of Olitski's abstract sculpture.

Oliski's folding color surfaces defy the literalness of edge and boundary. There appear to be no broken surfaces. Greenberg writes, the grainy, tactile surfaces of color contrive an illusion of depth as if those surfaces expand to contain a "world of color" and light differentiations impossible to flatness, but manage in some way not to violate flatness. Olitski's "free" shapes and contours perhaps constitute the first attempt in the history of art to realize pure color in three dimensions. Color does not merely lie on Olitski's hybrid surfaces, but creates a new kind of enriched surface and new spatial relationships. Resembling Kawaguchi's molten configurations, each surface becomes a total field of shape and form that avoids the determinate edges of the rectangle in its flowing, folding convolutions. Olitski ability to identify fluctuations of color value and hue makes spatially developed 3D figures appear like shaped color (as opposed to mere colored sculpture). Consequently, we may view his work in hybrid pleated surfaces as a precursor to Kawaguchi's multiple surface permutations.

Also, in a rare moment of self-criticism, Greenberg admits that he may have been altogether wrong about sculpture and 3D art, that "construction-sculpture," or "drawing-in-space sculpture" in the late modernist period is making itself felt as the most representative, fertile visual art of our time. Its no short leap to the assumption that Greenberg permitted mixed-media hybrids to salvage formalism in the 1960s, which later gave birth to its left branch alternatives in postmodern and simulation art. As Thierry de Duve (1996b) concludes from his study of 1960's art polemics, two dimensionality is the last specific refuge of modernist painting, but three dimensionality is the domain of the new, generic, hybrid arts.

In Mutation (1993), Kawaguchi's color surfaces seem to emit their own space and light within themselves (enfolding space and light), rendering them eerily weightless. This effect of enfolding, then unfolding space and light (of disposing forms in space) is partially the result of Kawaguchi's subtle chiaroscuro hue and shading, which produces an added illusiveness. Deleuze describes the chiaroscuro effect, the way the folding surface catches illumination and varies according to the hour and the light of day, as a function of the fold of matter and texture itself. Following Leibniz, Deleuze affirms that the fold affects all materials (metal, paper, fabrics, water, living tissue, the brain), because it determines and materializes form, becoming "expressive matter" with different scales, speeds and vectors. Since folding and the chiaroscuro effect are Baroque traits, Kawaguchi's folding, pleating surfaces of color can be said to resemble the overlaying folds and depths (crevices) of fabric or paper. Deleuze defines three types of inflection of the fold: 1) the ogive, or the pointed arch, that expresses the lines and valleys of flowing liquid, 2) the morphological forms of living matter, such as the dovetail, the butterfly and the hyperbolic or parabolic umbilicus, and 3) the vortical inflection of the variable curve, such as Koch's Baroque curve, that opens up on infinite fluctuation and permutation. The pattern of contraction of the latter complex spiral folds follows a fractal mode by which new turbulences are inserted between the initial ones. In its extreme form, the growing turbulence of folding ends in a "watery froth" and the erasure of recognizable contour. As Deleuze says, the Baroque is an "operative function" or "trait" which endlessly produces folds, then twisting, turning, and pushing them into infinity, fold over fold, one on the other.

Kawaguchi's abstract forms are therefore elastic bodies in space whose cohering parts that form a fold, or a multiple modulating surface of color. The fold does not appear to be separated into parts, but may be divided into an infinity of smaller and smaller folds (an endless folding, a 3D origami form). Baroque folding and chiaroscuro effects become an aesthetics for a kind of liquid architecture of 3D objects and spaces whose goal is curvilinearity, the twisting line, the fluidity of matter and the elasticity of bodies.

Whether they are found in abstract sculpture, the contours of nature, or 3D simulated cyberspace, Deleuze (following Leibniz) likens these complex folding interactions (inflections) to the solid pleats of a "natural geography": the curves of conical forms that sometimes end in a circle or an ellipse, or sometimes stretch into a hyperbola or a parabola (1993, p. 6). He may also be drawing on the continuing twentieth century interest in the curved spaces of non-Euclidean geometries (such as Beltrami's hyperbolic geometry) and new fractal geometric models. Eisenman (1993) is inspired by Leibniz's turn away from Cartesian rationalism and in his depiction of the point of the fold as the smallest element in the labyrinth of the continuous. Eisenman also acknowledges Deleuze for articulating a possible new relationship between vertical and horizontal, figure and ground, breaking up the existing Cartesian order of space in digital worlds.

Eisenman identifies Gilles Deleuze and René Thom as the two most important contemporary theorists of folding surfaces. Deleuzean extension is the outward movement of objects or events along the surfaces of planes, rather than downward in depth. Meaning is found at the surface; deep essences do not define forms. Eisenman recounts how Deleuze conceptualizes the idea of the surface object/event in the objectile, a contemporary technological object such as any object that inhabits 3D cyberspace. The surface object goes beyond the static framing of space: it necessarily includes the temporal and topological variation of matter.

Similarly, in Thom's mathematics, the variable curvature of the fold/unfold is the inflection of the pure event. Transformations of objects or events do not occur according to a privileged plan of projection, but instead are modeled by the neutral surface formed from a variable curvature or fold. A complex folding and unfolding can explain abrupt changes in form, which can even be used to explain sudden or catastrophic events. Eisenman explains, while a tiny grain of sand can trigger a landslide, we already see the conditions leading up to the moment of movement to be in place in structure or form. The fold in this sense contains aspects of both figure and ground, but cannot be reduced to the singular existence of figure or ground by itself. In a media age, the changing surfaces of 3D objects in cyberspace are never meaningful as static entities, but in their timely interaction in configuration with one another.

The formalists' concern with the form, contour, texture and relationality of flat and enfolded 2D surfaces is extended in Kawaguchi's 3D animations, where curving, hyperboloid or other stretchable or deformed topological surfaces emerge and take shape. Folds and hyperbolas comprise the substance of transformations and inflections of objects and events in 3D computer architecture; a modulating, synthesizing, liquid architecture capable of representing abstract constructions in digital, symbolic spaces. Deleuze suggests that the "fold" is a series of convergent points, or events, on a liquid surface, affirmed by difference. In The Logic of sense, Deleuze (1990) discusses how the ancient Epicureans failed to understand the quasi-causal nature of folding surfaces; they failed in developing their theory of envelops and surfaces, because they did not reach the idea of incorporeal effects. Their simulations remained subject to the single causality of bodies in depth. The Cynics and Stoics, however, learned that sense appears and is played out on the metaphysical surface of ideas, in the topological field of singularities, representations, pure events and paradoxes. Meaning resides on the surfaces of abstract objects and spaces, on the level of appearances.

Consequently, both ideas and their effects are superficial in simulationist new media that express seriality and reproduction: The "depth" of meaning is realized on the surface in the domain of visual, auditory and tactile representations, just as the three-dimensional space is represented in a two dimensional image or projection, which once flattened, can be mapped/morphed from object to object in 3D rendering. Kawaguchi's 3D computer art centers on a pure physics of surfaces, whereby events of a liquid surface depend on digital transmutations on the level of code, in auto-multiplying growth algorithms, but also on variations of a surface appearance of the simulated, ideational quasi-cause. His emphasis on surfaces translates consequently into a strong reliance on image mapping and ray tracing techniques to create photorealistic, 3D effects in his completed work or sequence.

Kawaguchi's liquid, biocosmic emanations also appear to be 3D representations of machine, biology and computer code. They seem to epitomize and embody Deleuze and Guattari's (1987) innovative and far-reaching revaluation of the machine/organism distinction in which the "machinic" is opposed to both the mechanical and organic to allow for complex, open-ended becomings within evolution. A truly "machinic" conception of creative evolution must embrace a radical pluralism of technical, semiotic, axiomatic and other machines that avoids the positing of the "human" and the reified, humanized notion of what constitutes autonomy on the machine. Perhaps Kawaguchi's animations are the earliest attempts to meet Deleuze and Guattari's "machinic" vision.

Kawaguchi certainly provides a topological, probabilistic and irrational animation space for his modulating folds and 3D forms. Each of these liquid volumes constructs with the others a noospheric "circulation" and a "cinema" of thought. Like philosophy, Deleuze believes that the interactive, animated cinema is a conceptual practice: In its twisting, folding and fissuring of digital, informatic substance, it constructs and discovers new pathways, connections and concepts. Although corporeal depth is important, Deleuze believes that each thing is inscribed, sublimated and symbolized on the liquid, noematic and metaphysical surface, the "second screen" or realm of informatics that "hovers" over bodies. He recognizes the brain as the "inductor" of that second, invisible, cerebral, parabolic, metaphysical surface on which all events fold and unfold. Thought brings about the projection, conversion and induction of a physical folding surface into a metaphysical surface; the projection in fact transmutes a Euclidean space into an abstract, topological space. Kawaguchi's recent animations, Mutation and Cell, confirm Deleuze's belief that creating new connections in art means creating them in the mind too!