3.1 How Can Process Be Defined?
As defining the notion of “process” is itself a process, a becoming rather than a being, the attempt to define process is somewhat paradoxical, and in this sense, I prefer the notion of an approximate generalizing description. The one I will present is contiguous on, or conditioned by, definitions given by many others before me.Footnote 1 This definition is meant to open up potential modifications or changes to cater for a variety of contexts and uses:
A process is any temporal sequence or flow of events or occurrences (process constituents) that are causally, conditionally or functionally linked to one another, such that the sequence of events shows temporal interdependence, leading to emergence, creativity and novelty.Footnote 2
A process must not be defined as some sort of modification of an independent thing, a typical substance (e.g., the process of running up a tree as a temporary feature of the independent thing called “squirrel”).Footnote 3
The intuitive model of a process, its “intuition pump” (Section 2.3.3.1), is the subjectless activity, expressed in sentences like “It is raining.” There is no independent thing, denoted by it, to which the activity of raining is applied. According to process ontology, there are only processes: this is the counterintuitive, hard-to-swallow part of this ontology, as our intuitive belief is that processes are impossible or inexistent if there are no things to which they apply, that “do” or undergo them. But this belief is nothing but a linguistic enactment of a grammar of nouns and verbs. The fact that this grammar suits our intuitions comes from our practical focus on processes that are self-sustaining, or self-reproducing for a long enough time to inflict the illusion of permanence and essence upon us.
3.2 Properties of Processes
Process descriptions are interest- or perspective-dependent. That is, in the inextricable tangle of processes that occur in the world for any duration, from the fastest on the scale of quantum physics to the longest on the scale of cosmology, I can focus on a particular process depending on my point of interest. For instance, I can either focus on the process of putting down a brushstroke, or on painting a painting, or on the process of stylistic changes in Picasso’s work, or in the evolution of art in the nineteenth century in France, or I can focus on the process of how these timescales are entangled (the list is basically endless).
Each of these processes which I can focus on and that I isolate from all others is in itself dependent on a virtually infinite variety of underlying constituent processes. On the level of the process of brushstrokes, underlying processes concern viscous molecular flows in the oil paint, the sensorimotor processes of brush handling, the process of slow oxidation of the linseed oil in the paint, and so forth (for a detailed description of a brushstroke as a complex dynamic system, see Section 7.2.2).
The events or occurrences that form the components of the process depend on the chosen level of description, the chosen timescale. According to the above definition of process, these components are causally, conditionally, or functionally linked to one another, such that the sequence of events shows temporal interdependence: on the level of brushstrokes, the next stroke of paint depends – in one way or another – on the preceding stroke(s) (comparable examples will be given for processes on all possible timescales).
Temporal interdependence implies that processes form iterative systems. An iterative system is a process in which every next temporal component, every next step or stage, is conditioned by the preceding components, steps, or stages. Iterativeness applies to all the possible levels of description, that is, to all possible timescales, and is a fundamental feature of dynamic systems.
A process, for instance painting-a-painting, is a pattern of occurrence, that is, a pattern of events that occur in time.Footnote 4 Specific patterns of occurrence originate from underlying “process rules,” that is, they emerge from more or less constrained principles of how a next step in the process follows from the preceding step(s), of how one step in the process creates a space of possibilities for the next step. An object, such as a work of art, is a pattern of occurrence, with a beginning, a long or short period of self-reproduction and deterioration, and an inevitable end.
Every step, stage, or temporal component in a process provides adjacent possibilities for the next steps, stages, or temporal components.Footnote 5 Adjacent possibilities enable as well as constrain the continuation of a process, that is, its immediate future. Adjacent possibilities thus determine the dynamics of processes, the way they emerge over time.Footnote 6 There are infinitely many ways in which such patterns, that is, specific, ordered sequences, can be realized, for instance in the creation of a painting. On the process level of applying paint, for instance, they can vary from paleolithic painters taking liquefied pigments in their mouth and blowing them onto a rock surface, to the highly planned, smooth finish of a French nineteenth-century academic realist painter, to Pollock’s seemingly frantic dripping of paint onto a canvas lying on the floor, to the work of an impulsively and highly physically working young contemporary painter.Footnote 7 On the level of a particular artist’s artistic evolution, specific adjacent possibilities are given by the works already created by the artist. Over the course of several consecutive artworks from an artist, we observe variation, and this variation is like a limited representation of the range of adjacent possibilities at a particular moment (e.g., the year 1901 in Picasso’s artistic career). It is a restricted representation of the range of possibilities, for the trivial reason that in a necessarily limited number of works of art,Footnote 8 not all the adjacent possibilities present at a particular moment in time can be actualized. What we see then is the range of adjacent actualizations given the actualizations up to that time (for instance, in the work Picasso actually created up to 1901). On the level of art history, we can discern successive as well as simultaneous stylistic periods, ways of creating art, that create possibilities for continuation as well as change.
The concept of adjacent possibilities is related to that of affordances, which was introduced in psychology by James Gibson in 1979.Footnote 9 Affordances are specific action possibilities or invitations for action provided by specific objects, spaces, persons, or contexts that present themselves in a concrete action or activity of a person, and that are picked up immediately, that is, without intermediary reflection or cognitive processing.Footnote 10 Works of art offer affordances for a whole range of activities, from creating new works of art, to artistic experiences of viewers, to commercial activities of artists and art traders. These affordances are objective properties of the work of art, given by its properties qua objects (e.g., their color, form, texture, physical appearance, conditions of maintenance and (im)permanence).
If the work of art is a performance, the affordances are typically social. An example of a social affordance is me asking you a question. When I ask you a question, I present you with a range of affordances, the most likely of it is you giving an answer, but the way you do so depends on how familiar we are with each other. In the 1960s, sociologist Harold Garfinkel developed ethnomethodology,Footnote 11 a way of studying implicit affordances in social interaction by breaching the tacit rules governing the way people interact (e.g., by silently staring toward a person who just asked you a question). This idea has been widely used in performances, such as Marina Abramović’s The Artist Is Present,Footnote 12 in which the artist was actually breaching the audience’s implicit rules of social interaction, in an attempt to create an experience of the here-and-now, which, no doubt, was highly colored by the specific context of display in a museum or gallery.Footnote 13 Affordances are always relational: they depend on the action possibilities of the perceiving agent, the agent’s ability to “resonate” with the affordances, that is, they depend on the agent’s effectivities.Footnote 14 In the context of art appreciation, effectivities imply learned dispositions and abilities to understand art, acquired strategies of artistic experience, and cognitive processing.Footnote 15 The immediacy of affordances may at first sight conflict with the nature of many art forms that require reflection and thought, such as conceptual art. However, in such cases, the affordance of the work of art consists in inviting very specific, art-related processes of reflection that will not spontaneously occur with other, very different types of work of art, for instance, Baroque paintings that are visually overwhelming, such as Rembrandt’s Night Watch or Rubens’ Descent from the Cross. Critics, art historians, and art professionals will have different effectivities than relatively “naïve” viewers or artists, and works of art will provide highly specific affordances for them, which can be communicated to artists and naïve viewers, potentially changing the affordances that a particular work of art presents for them.
Processes interact in the sense that they interfere with one another and are determined by these interactions. Because processes can interfere, and do interfere constantly, they tend to form complex webs, extended across space and time. For instance, painting-a-painting or creating an installation is a web of intertwined, constituent processes, and is itself a component of a much broader web of art distribution and interpretation, that is, of what is often called an artworld. A process is therefore a particular pattern of coordination of constituent processes or events, across many interacting timescales (from very short- to very long-term).
In terms of the nature of their time course, processes can have various temporal properties. For instance, they can proceed in a smooth, continuous and gradual way, or they can show sudden jumps, switching points, or discontinuities. These properties can occur on short-term timescales, such as the duration of the creation of a particular work of art, or on long-term timescales, such as historical changes in artistic styles. These temporal properties, and how they result from underlying and overarching processes, is the topic of Chapters 6 to 11.
Interacting processes have particular generative properties: they form patterns of interaction that are self-sustaining over a certain, characteristic time span. They generate emergent, novel, and creative properties. All this is the domain of complex dynamic systems theory (see Section 3.4).
In complex dynamic systems – and art is undoubtedly a complex dynamic system – the temporal and generative properties of processes are the result of their underlying dynamics, that is to say, of the way the components of the process interact and influence one another. That is, these temporal properties are generated by the process itself and are not imposed on it by external accidents or factors, or by some external controlling agent: processes organize themselves through their interactions (in technical jargon, we can say that processes self-organize, see Section 3.4.4). These underlying dynamics allow us to build “a general science of the processes underlying and controlling the behavior of apparently very different situations,”Footnote 16 ranging from biological processes, to human development, or to art. Let us first focus on the properties of dynamic systems and then move to complexity and complex dynamic systems.
3.3 Dynamic Systems of Art
3.3.1 A Basic Definition
Although the theory of dynamic systems comes from mathematics, the conceptual core of dynamic systems can be intuitively understood relatively easily. Formally a dynamic system is defined as “… a rule for time evolution on a state space.”Footnote 17 For instance, the creation of a work of art is a time evolution, that is a sequence of events such as brushstrokes, corrections, thoughts, perceptions. The history of art is a time evolution, consisting of events in the form of works of art with particular stylistic properties, interpretations by art experts, and so on.
3.3.2 Evolution Rules
The time evolution is driven by a mechanism of change, by a force or forces causing change, called the evolution rule(s). In real systems, such as those of creating works of art, the evolution rule is a complex web of causal and conditional factors – of adjacent possibilities – that make one action follow another action, for instance that make a particular brushstroke follow a preceding brushstroke.
3.3.3 The State Space
The state space “is the set of all possible states of a dynamical system; each state of the system corresponds to a unique point in the state space.”Footnote 18 In its simplest form, a state space may be a finite set of states. For instance, the possible states of a work of art are inexistent-in preparation-unfinished-finished-destroyed. In the state space, the evolution rule explains why a work of art moves from one of these states to another.
But the common form of a state space in dynamical systems is that of a certain number of continuous dimensions (a finite dimensional spaceFootnote 19). For instance, my movements form a dynamic system requiring a three-dimensional state space: coordinates of length, width, and height from a given point of origin. Whereas the description of real space in terms of three dimensions may be a physical necessity, the state space of a complex system such as visual art is a matter of personal perspective, of a describer’s interestFootnote 20 (see also Section 3.2). For instance, Heinrich WölfflinFootnote 21 described artistic style during the sixteenth and seventeenth centuries in terms of five dimensions: (i) linear/painterly, (ii) planar/recessional, (iii) closed form/open form, (iv) multiplicity/unity, and (v) absolute clarity/relative clarity. They can be treated as continuous dimensions, for example, from maximally linear to maximally painterly, or from maximally closed to maximally open, with everything in between. If you combine two such dimensions (which are easily represented on the flat surfaces of a book page or screen), you obtain a two-dimensional space. Art historians can choose to represent all works of art produced during a particular period or point in time by an average value on each of the dimensions, for example, the average linearity and average openness of all the paintings created between 1600 and 1620. They can choose to represent each painting separately, according to that painting’s values on the painterly and openness dimensions. This will result in a particular period being represented by a cloud of points (the cloud of all paintings during that epoch). The average position of the cloud of points will change over the course of time and the sequence of these changes forms a trajectory in the state space (see Figure 3.1). Since Wölfflin described five dimensions, or properties of paintings during the sixteenth and seventeenth centuries, stylistic changes during that period can thus be thought of as a trajectory in five-dimensional space.
Figure 3.1 A state space consisting of dimensions open form/closed form and linear/painterly. The state space represents two groups of painters (black dots and white dots). “Black” painters move in the state space from a closed form/linear approach to a painterly/more open style; the difference between the painters increases; “white” painters move from an open form/linear approach to a closed-form/painterly approach; the differences between those painters decrease (they tend to adopt a more uniform style over the course of time); trajectories over time (e.g., a period of 20 years) are represented by black and dotted arrows respectively.
Contemporary researchers use artificial intelligence methods to discover stylistic dimensions of works of art over the course of time. It is interesting to observe that these automated methods converge on the intuitive distinctions represented in Wölfflin’s dimensions.Footnote 22 These methods can also uncover new dimensions – that is, spaces of potential variation of works of art – such as entropy (disorder) and complexity.Footnote 23 Dimensions can be derived from psychological frameworks for the assessment of art attributes,Footnote 24 or from any theoretically justified framework of description.Footnote 25
3.3.4 A System of Dynamically Coupled Dimensions
In a dynamic system, the dimensions of the state space are coupled by means of evolution rules. For instance, in a state space described by Wölfflin’s dimensions, a change toward a more painterly approach (one dimension) in the works created by a particular artist might provide an adjacent possibility for more open forms (another dimension), and a change toward more open forms provides an affordance for a more painterly style (in this example, the coupling between these two dimensions is reciprocal, or put differently, it is a loop from one to the other and back).
Dynamic couplings can create unexpectedly complex patterns. A famous example outside of art is Lorenz’s extremely simplified model of the weather system, based on the dimensions convection rate, horizontal temperature variation, and vertical temperature variation (Figure 3.4). These three physical properties affect one another in relatively simple ways and result in a very complex trajectory in the three-dimensional state space.Footnote 26 Here is an imaginary example from art: suppose that there is a group of artists with an urge to innovate, but they are also sensitive to the reaction of their public. If the public is conservative and rejects their innovations, the artists will tend to reduce their innovative tendencies, maybe returning to their familiar style to please their public. This simple dynamic can be expressed in the form of two coupled mathematical equations (technically, a predator–prey model). Depending on the value of their parameters (e.g., how strong is the urge toward innovation, how strong is the public rejection of novelty), these equations either lead to a stable equilibrium between the level of artistic innovation on the one hand and acceptance/rejection by an audience on the other hand, or they lead to a repetitive cyclical pattern in which innovation and acceptance/rejection will go up and down (see Figure 3.2).Footnote 27
Figure 3.2 A dynamics resulting from tensions between the state space dimensions of artistic rejection–acceptance and conformism–innovation. The state space dynamics takes the form of a loop or flattened cycle (top). On the time axis (middle and bottom), the dynamics shows cycles of innovation and rejection; dependent on the way the dimensions interact, the dynamics may settle into a constant value of relatively low innovation and relatively strong rejection of novelties (forming a point attractor in the state space) (bottom).
Figure 3.3 A change in activity implies a change in the underlying attractor landscape. In figure (a), an imaginary painter, Vincent, is painting a landscape, and the activity is self-maintaining. Meanwhile, Vincent is getting more and more thirsty and craving for absinth (the control parameter), which provokes a change in the attractor landscape (b), leading to a sudden switch from painting to drinking in the pub (c). In figure (a) pushing the system toward the left (e.g., a friend inviting Vincent to go to the pub) will only have a temporary effect. As soon as the friend is gone, the system (Vincent) will roll back to its original position (the system is stable and resilient).
Figure 3.4 Four states in the development of a Lorenz attractor, which is based on three coupled variables; the curves represent the trajectory of the system (represented by a black dot) over the course of time in two dimensions; over time, the trajectory of the system becomes increasingly complex. It moves toward and away from two points in the figure (represented by the small crosses in the third state).
The dimensions of a state space may also be described as nodes in a network and the coupling between the dimensions as directed relations between these nodes (e.g., an influence from component A to B). Although state space and network descriptions are formally equivalent, we will see that network descriptions are preferable in the context of complex dynamic systems operating in a multidimensional state space. A two-dimensional state space can be easily visualized; three dimensions often require computer animations and thus exceed the possibilities of figures in a book, and from four dimensions on, visualization is almost impossible (unless one reduces the dimensions to only two, for instance, one focuses on only two of Wölfflin’s five dimensions). On the other hand, a network of 5, 10, and many more dimensions can be easily visualized to show how these dimensions affect one another. The disadvantage is that networks cannot represent patterns of change over time (one can use computer visualizations to do that). All this is important, since visualization plays a highly significant role in understanding complex systems.
3.3.5 Iterative Systems, Evolution Rules, and Art’s Affordances
3.3.5.1 Preceding State(s) Conditioning Successive State(s)
A dynamic system is an iterative system (see Section 3.2): every next state is conditioned by the preceding state(s). Put differently, the next state is a “function” of the state(s) by which it is preceded, and this function is given by the system’s evolution rules (Section 3.3.2). This abstract notion of “function” can take different forms.
The next step, state, or moment in an art process can be a simple continuation of the preceding process, such as when a particular artistic tradition is continued (eventually for a very long time, think of cave and rock paintings, or the form of Egyptian tomb murals).
The “function” can also involve some sort of smooth transformation of what precedes it (e.g., a gradual evolution of a particular painting style).
It can involve a radical break (as any radical break is a break with something that preceded it, and to which it opposes itself), or it can show any other form of discontinuity that is typical of the way complex dynamic systems can self-organize and generate emergent, that is, unexpected properties.
The way a preceding state conditions the next state may vary from the preceding state strictly determining the next one, to the preceding state offering opportunities for, or constraining the possibilities of the next state. The latter is what we expect to happen in art processes. The preceding state may offer a range of possibilities for the next one, with a typical degree of freedom for creative processes to occur. This is what theoretical biologist Kauffman called adjacent possibilities (see Section 3.2). The preceding state may also limit or constrain the next step or state, that is, condition the next step by strongly limiting its range of possibilities. One step or state in a process may provide specific affordances for action, that is, for creating the next step or state.Footnote 28
3.3.5.2 Preceding States Offering Affordances for Next States
In What Art Does, Ryan Wittingslow proposes a theory of works of art as tools for meaning, based on the concept of affordances: “… while artwork functions are fixed by the intentions of the artist, artwork affordances are furnished by a virtuous confluence between the features of the artwork, the codes that constitute the artworld, and the various capacities of the members of the artworld public.”Footnote 29 That is, affordances are relational properties, existing in the dynamics of the artwork–person interaction, which is embedded in an interaction with a context, an artworld.
Already in 1961, in The Shape of Time George Kubler presented a fundamentally processual and dynamic account of the visual arts as part of visual culture. Much of what the book puts forward and explains can be directly translated and interpreted into the language of modern dynamic systems theory. For instance, Kubler uses the notion of the self-signal in a way that is very similar to the concept of affordances. The self-signal of a tool like a hammer, or the self-signal of a painting, is the kind of activity that the tool or painting in question “signals”; it is an immediate invitation to use or apply the tool or painting in a particular way.Footnote 30 The affordances of a work of art are of a very different nature than those of a standard physical tool such as a hammer that Kubler uses to explain the notion of the self-signal.Footnote 31 In the case of the physical tool, they are the immediately perceived affordances for specific tool use, which depend on the abilities and interest of the potential user (a carpenter or a murderer in an Agatha Christie novel). They may be affordances for a museum visitor, or for an art critic for whom a particular work of art serves as the basis of a whole range of activities in the form of critical or interpretive essays. Each of these affordances leads to specific activities that provide their own affordances for art-related activity, thus creating an iterative sequence of activities, of events in the state space of art.Footnote 32 For an artist, works of art made earlier may provide affordances for reproductive artistic activity, creating new works of art that reproduce fundamental features of the work of origin with often only small variations. In essence, such activities are forms of “copying” and replication, and at the same time they are exploring the range of possibilities, including the boundaries of the variation given in the work of art that provides the starting point (see examples in Section 2.1). However, earlier works of art may also provide affordances for innovation, that is to say for more or less radical transformation or variation of the original starting point, resulting in a work of art that Kubler calls an “invention,” a truly creative discontinuity in the stream of works of art. This discontinuity is inevitably linked to its predecessors. It is a reaction or opposition to or transformation of those predecessors (earlier works of art) on a deep or radical level. Kubler calls the important visual inventions, that is to say, truly novel visual forms providing a novel solution to a particular problem of visualization; prime objects.
What Kubler describes as a single prime object can in reality be a small collection of exemplary or inspirational works of art where the principles of a new art form are present in nascent, often relatively implicit form, to be made explicit by the linked sequence of works of art that follow from it. Picasso’s Les Demoiselles d’Avignon may be seen as a prime object in this regard, a paradigmatic and inspirational work that formed the starting point for later cubist work. However, the painting itself was preceded by a lot of sketches and preparatory studies made in the years 1905 and 1906. They are all part of the iterative sequence of products of visualization, of Picasso’s temporally linked attempts to solve a particular artistic problem that most likely only became explicit as he worked on its solution in a sequence of steps, opening new opportunities or showing dead ends.Footnote 33 Picasso’s studies themselves emerge as part of an iterative sequence of works of art by others, in which various lines converged. For instance, one is the work of Paul Cézanne, and in particular Cézanne’s The Large Bathers, that Picasso must have seen in 1907. Other lines concerned the African masks that Picasso saw at the then-dusty and unattractive Musée d’Ethnographie du Trocadéro in Paris.Footnote 34 It remained like that until the 1990s, after which it was replaced by the impressive Musée du Quai Branly – Jacques Chirac, which in itself is a great illustration of how art originally despised as “primitive” was elevated to an entirely new status of value by the creation of a prestigious art temple that formed its new embedding space (an ontological shift, basically).
The iterative link connecting African masks or Cézanne’s Bathers to Les Demoiselles is, in all likelihood, itself a rather complex, multifaceted process, the nature of which is concealed by simplifying phrases like “Picasso was inspired by…” (I will discuss inspiration in Section 8.4.6). Gikandi,Footnote 35 for instance, argues that Picasso loved the idea of the primitive and the tribal, whereas his opinion about the makers of those objects would currently be considered outright racist and despising. Nevertheless, the figuration from the masks reappeared in at least one of the Demoiselles, which implies that there is a link of conditionality or enablement between his seeing the masks and his painting the final version of the Demoiselles d’Avignon (who were, in spite of the title, not misses from the Southern French city of Avignon but prostitutes from a brothel in Avignon Street in Barcelona, a provenance that adds to the brutalist appearance of the painting).
Alfred Gell’s Art and AgencyFootnote 36 sketches an interpretive framework that shares many elements with the theory of complex dynamic systems (although the terminology he uses is quite different). For Gell, art is process, a view that plays an important role in anthropological approaches to art.Footnote 37 He describes the art object as a particular type of “agent” characterized by what it does, the way a human agent does things (which implies that the ontological foundation of this theory is processual). In the section on the artist’s oeuvre as a distributed object,Footnote 38 Gell described a scheme that can easily be subsumed under a dynamic systems umbrella: it is a network of works of art, that is, preparations for works of art and reflections, that functions as nodes providing protentions (adjacent possibilities, outcomes of iterative functions) and retentions (elements that refer to earlier works or states in the system).
In The Psychology of Contemporary Art,Footnote 39 Minissale discusses art’s affordances in the context of the brain, more particularly in the form of the conceptual and discourse affordances of a work of art given to an art appraiser.Footnote 40 He is also referring to the fact that our actions are based on affordances, while at the same time those actions continuously create new affordances, thus creating iterative sequences on various timescales.Footnote 41 We have seen that affordances require abilities or “effectivities” from the part of an agent, for instance, knowledge about interpretive frameworks for works of art.Footnote 42 A painting like Yellow-Red-Blue by Wassily Kandinsky (1925) requires at least some knowledge of the aesthetic principles that Kandinsky elaborated in a theoretical book published in 1926.Footnote 43 Minissale also emphasizes that the interpretation of a work of art, its appreciation in the form of creating new schemata that enable the understanding of a particular work of art, is in itself a creative process.Footnote 44 Affordances for the experience of art will thus develop along with the development of interpretive schemes for art, patterns of art experience. This development will take place on the timescale of an art appraiser’s personal development, which depends on age and artistic and cultural learning. It will also take place on the historical timescale, in a process of mutual influences between the creation of art and the way it is experienced. In The Global Work of Art,Footnote 45 Caroline Jones shows how the nature of art experience and participation has changed in relation to changes in the presentation of art to a public in the form of world fairs and biennials, in relation to changes in the nature of the works of art presented (with an increasing focus on works of art as events, and participatory events in particular). These three aspects (experience-presentation-creation) form a long-term, dynamic system of mutually influencing components (see also Figure 3.5).
Figure 3.5 Linear couplings and loops between three components: creation of art, presentation of art, and experience of art.
3.3.6 Attractors, Stability, and Change in the Visual Arts
3.3.6.1 The Concept of Attractor
Recall that in a dynamic system, evolution rules turn one position in the state space (that represents the current state of the system) into a next position (a next state), then turn the latter into yet another one, and so on, thus creating a trajectory in the state space. A typical characteristic of dynamic systems is that such trajectories tend to evolve toward special positions or states: the evolution rules will turn this position into a next position similar to the previous one. That is, dynamic systems tend to evolve toward states in the state space that are self-reproducing (with only small variations around the self-reproducing theme). Such states are also self-maintaining: if they get disturbed by some external cause (a perturbation, such as a strong negative reaction of a critic), they tend to return to the position where they came from (they tend to be resilient). These positions, states, or small regions in the state space are called attractors. That is, attractors are stable states, in a specific state space, created and maintained by the evolution rules of the system. This means that stability, that is, periods where nothing fundamentally seems to change, are as dynamic as periods of rapid change: periods of stability require active reproduction and maintenance of the status quo. A real system is always subjected to increasing entropy, that is, to spontaneous disintegration and decay (according to a very basic law of physics, namely the second law of thermodynamics). In order to counteract these forces of decay, complex systems of energy-consuming activity are needed.Footnote 46
Examples of attractors in art are stylistic periods or schools, such as Baroque, Romanticism, Classicism, and impressionism, which are characterized by relative historical stability of artistic principles or views on creating art. These principles or views can be specified in terms of state spaces that describe stylistic aesthetic properties (e.g., Wölfflin’s five dimensions), philosophical properties (e.g., art as a self-reflective process), ideologies (e.g., art as promotor of gender equality), and so forth. Any specific work of art itself is an example of an attractor: during the process of its creation by the artist, the activities of creation evolve toward a specific visual-conceptual form (the work’s finished form). Self-reproduction and self-maintenance of this form also depend on the way an art public, including critics and art theorists, consolidate the visual-conceptual form in their experience of the work of art, as Dewey has noted. Of course, the mere visual properties of the work of art qua object might be quite robust and change only as the result of aging, damage, restoration, etc. However, the work of art is not equal to the mere physical object that represents it.Footnote 47 What makes a particular object a work of visual art is the combination of the visual form of the work as object and the physical, cultural, and conceptual and interpretive framework in which it was created and in which it is (later) understood and experienced. This network of components forms an attractor that tends to change over the course of time, in the form of temporary stabilities and gradual as well as discontinuous shifts (e.g., the nineteenth-century rediscovery of Vermeer and Hals by the French art critic Théophile ThoréFootnote 48).
According to Francis Halsall,Footnote 49 important artists are attractors, in the sense that art history tends to evolve toward a format of interpretation and evaluation that – at least for a certain period of time – tends to be self-reproducing and self-maintaining. During his lifetime, Vincent van Gogh occupied a zero-position in the state space of dimensions that describe “exceptional” or high art (it was simply not recognized as important art). After his death, a number of events occurred that projected his art into a self-reproducing and self-maintaining region of the state space of important art. It started with the work of Vincent’s brother Theo, which was then taken over by his widow Jo van Gogh-Bonger, followed by curators of the Amsterdam Stedelijk MuseumFootnote 50 and finally by art historians and public all over the world. The financial value and commercial interests assigned to a particular artist strongly contribute to the artist’s self-reproducing and self-maintaining attractor position in the system of the arts.
3.3.6.2 Attractor Landscapes
Attractors are situated in attractor landscapes, comparable to a real landscape of hills (the unstable states) and valleys or wells (the stable, self-maintaining attractors). An attractor landscape is a heuristic device, a way of visualizing various aspects of a complex system with a single metaphor, to which mathematical formalizations and empirical predictions can be applied. An attractor landscape can be as simple as a single attractor and be as complex as a rugged mountainscape. Attractor landscapes emerge from the interactions of the myriad of events, forces, and components that constitute and influence a particular complex system, for instance an artworld embedded in social, cultural, economic, and political systems. Think of an attractor landscape as a flexible sheet. Under this sheet, we find a whole system of strings and supports that are connected with one another, and they pull and push the flexible sheet into a specific form of hills, wells, and valleys, that is, its attractor landscape form. As long as the underlying system of forces – that is, the complex dynamic system itself – does not change, the attractor landscape keeps its form. However, once the system of underlying forces undergoes a change, for instance as a consequence of a prolonged stressor, or the introduction of new technological or social possibilities, the landscape will change, and new attractors will emerge, forming a new landscape. This will create new possibilities for the system in terms of possible attractors.Footnote 51
The current state of the system is visually represented by the position of a ball that tends to roll spontaneously toward the nearest lowest point (hence the notion of “attractor”). Think of the ball as being subjected to the force of gravity, which is a metaphor for the fact that systems are drawn toward the nearest state of minimal free energy or minimal uncertainty.Footnote 52 This being drawn in a particular direction (the attractor) is caused by the evolution rules (the mechanisms that make the system move or change). The concepts of state space, evolution rule, attractor, attractor landscape, and momentary state of the complex system are thus intimately connected with one another, as different perspectives on the same phenomenon (see Figure 3.3).
3.3.6.3 Attractors as Ways of Describing Stability and Variability
An attractor provides a way of describing stability and variability. Nothing in the world is ever absolutely stable, there is always variation, because real systems are always subjected to accidental influences (called perturbations). The form of the attractor – deep versus shallow – determines how the system will react to such perturbations: with much variability in the case of shallow (Figure 3.3(b)), and little to almost no variation in the case of deep attractors, that is, stable systems (Figure 3.3(a) and 3.3(c)).
The possible variability of a system also depends on the total form of the attractor landscape. A landscape with only one attractor entails considerably less potential variation than a system consisting of two or several attractors. Variability also depends on how the system moves across the landscape, that is, metaphorically, on how the rolling ball behaves. In real systems, several types of motions may be distinguished.
To begin with, an attractor may have the form of a single point in the landscape (the deepest point of a valley or well), or of more or less bounded regions in the state space (like a flat valley floor). In the first case, variability tends to be low (if the attractor is deep enough); in the second case, variability is high but bounded by the surface of the valley floor (Figure 3.3(b)).
An attractor may take the form of a cycle, that is, there is continuous change, but the system will run through a similar set of states (for instance a>b>c>b>a>b … in Figure 3.3).
Finally, an attractor may take the form of a chaotic or erratic trajectory through the state space (e.g., the Lorenz attractor of the weather system, see Section 3.3.4 and Figure 3.4). Note that the mathematical description of attractors, with the distinctions between point, cyclical, and chaotic attractors, can only be applied in an approximate sense to real attractors. For instance, in the real and messy world, chaotic attractors such as the Lorenz attractor will be difficult to distinguish from random variation around two points of attraction that never stabilize.
3.3.6.4 Types of Attractors and Types of Change
What sort of attractors can we expect to find in a complex system such as art? Kelso and his coworker TognoliFootnote 53 present a general framework, applying to all kinds of complex systems, which distinguishes mono-stable, multi-stable, and metastable processes, giving rise to different types of attractors (defined as temporarily self-sustaining emergent patterns).
Mono-stability means that the system self-organizes into one attractor, a stable, coordinated and self-sustaining state: a robust pattern of creation, meaning, or interpretation that can withstand relatively strong perturbations. On the long-term timescale, the art of Ancient Egypt forms an example of a long-term attractor of style, content, and function, as it remained remarkably stable for about six millennia, relatively insensitive to potential influences from outside (perturbations). If art were a mono-stable attractor, all forms of art would be small variations of one dominating style. Attractors may occur in sequence, which complies with the standard interpretation of art history as a sequence of periods or styles, each with their own unique attractor. Successive attractors may also apply to specific artists. A historical example is the work of Lawrence Alma-Tadema (1836–1912), painter of the life of Romans and Greeks who was considered one of the major artists of his era, was then for a long time considered ultimate kitsch,Footnote 54 and is now showing a revival of positive interpretationFootnote 55 (one attractor is replaced by another one, which is replaced by the first). Comparable cyclical patterns may also occur on the very short-term timescale of rapid alternations between admiration and repulsion when a specific person perceives and evaluates a particular work of art, for example, a typical example of nineteenth-century art such as Cabanel’s Birth of Venus, or contemporary works such as Manzoni’s Artist Shit or Abramović’s Rhythm 0.Footnote 56 However, one may argue that such rapid alterations only take place if both attractors – admiration and repulsion – are part of the same multi-stable attractor landscape (see also Figure 7.15).
Multi-stability implies the simultaneous existence of different attractors, that is, different patterns of artistic meaning and evaluation.Footnote 57 The simplest example is bi-stability: an attractor of serious art and an attractor of nonart, kitsch, or crap. For instance, if contemporary art were represented by a bistable attractor landscape, Damien Hirst’s 1996 Home, Sweet Home could be great and important art for some and utter crap for others.Footnote 58 Multi-stability often implies differences in what is technically called the depth and width of an attractor, that is, the strength of resistance of the attractor to perturbations (e.g., critique) and the generality of the attractor (e.g., the number of art critics agreeing on a particular interpretation; the consensus of art experts on Home, Sweet Home is an example of a deep and wide attractor in the landscape of artistic interpretation and evaluation; see Figure 3.3(a), 3.3(b) and 3.3(c), for an example of deep/shallow and narrow/wide attractors).
Finally, attractors may be metastable, that is to say that they are “beyond” stability. That is, they encompass various possible states of organization, that is various possible attractors, each of which carries an intrinsic tendency toward other states. Metastable states imply complementarity,Footnote 59 for instance a simultaneous state of rejection and admiration, or simultaneity of apparently mutually exclusive interpretations. If a work of art embodies metastability, it will be dynamically ambiguous, fuzzy, and multiform. “Dynamically” means that various possible interpretations or evaluations are connected in the time course of a particular artistic process, in which one interpretation invites the other, and vice versa, from short-term art experiences by a particular viewer to long-term interpretations and evaluations in art history. Home, Sweet Home forms a metastable attractor if ambiguity and complementarity form the essence of its associated artistic interpretation, that is, if its emergent artistic meaning incorporates that it is both high art and crap. In that case, the work provides a specific affordance, namely the invitation to explore opposing tendencies and incompatibilities. For some, this exploration might evolve toward a mono-stable attractor (in the end, it is high art for some, it is crap for others, and still others solve the complementarity by an attractor of indifference, see Figure 7.15).
Metastability and multi-stability are associated with critical transitions: a system can easily switch from one state to another and back as a consequence of small random perturbations (accidental events) or as a consequence of deliberate decision.Footnote 60 For this reason, states of multi- or metastability can also be called critical states. Many complex systems, and art is probably an example of them, tend to self-organize not to mono-stable states per se, but to critical, multi- and metastable states (self-organized criticalityFootnote 61), which is a state from which different interpretations – even incompatible ones – are possible. It is likely that this tendency toward criticality is an essential condition for flexibility, adaptivity, and creativity of complex systems. The brain, for instance, self-organizes toward critical states, that is, states of metastability in order to maintain flexibility and adaptivity to new, rapidly changing circumstances, on very short timescales.Footnote 62 A particular work of art may increase its appeal by exploiting this property of metastability (see Section 4.2.5).
3.4 Complex Dynamic Systems: Cyclical Coupling, Self-organization, Nonlinearity, and Emergence
3.4.1 A Basic Definition
A complex dynamic systemFootnote 63 can be described as
a collection of many interacting components that self-organize into patterns of activity of the system as a whole. These patterns emerge from the interactions between the components, but their properties cannot be reduced (e.g. by linear superposition) to properties of the latter. In a complex dynamic system, the emergent properties of the whole, first, affect, constrain and enable the underlying processes from which they result, and, second, interact with other emergent properties.
A human being, for instance, is a complex system of interacting components: sensory organs, brain, nervous system, limbs, muscles, etc. They interact with one another and change through these interactions (muscles become weaker or stronger, the brain becomes more specialized through learning, etc.). These interactions self-organize into an organism, and organisms can act in their environments. This action is an emergent property of the underlying organismic processes, constraining and enabling their functioning (e.g., what I do depends on what my muscles do, but what my muscles do depends on what I do). A human being is a component of a complex system on a larger scale, namely a community consisting of interacting individuals (e.g., a family, a local community). Social communities interact with other communities in a larger scale system, for instance, a city or nation, or the human population. Each of the components of a single human being (e.g., an organ or a brain) is a complex system in itself. A brain for instance consists of nerve cells that interact with one another and self-organize into a system with emergent properties, such as consciousness or planning of activities that interact with the emergent properties of the body as a whole, namely its functioning as an organism.
This example illustrates two important principles that we already noticed in the description of processes.
First, a complex system depends on a particular perspective or point of interest: we can take persons as components of the system we are interested in. However, every such component is a complex system in itself and every complex system can serve as a component of an overarching complex system. This is the property of recursiveness.
Second, complex systems operate on various interlocking timescales, for instance processes on the level of milliseconds in the brain, or actions on the timescale of minutes, or changes on the timescale of years or centuries. Timescales are interacting: what happens on the timescale of activity, such as the creation of a work of art, depends on processes that have taken years, decades, or even centuries to develop (e.g., specific art styles or patterns of performance or activity that define what counts as art). On their turn, these long-term changes depend on a myriad of short-term processes, namely the actual creation of works of art and the processes of their appreciation. Some of these short-term processes may drive relatively rapid historical rapid changes (e.g., the famous Brillo boxes that served as turning points in the nature of visual art), whereas others are consolidating the existing artistic style or characteristic pattern (e.g., paintings, installations, or performances that are variations on existing paintings, installations, or performances).
A typical feature of a complex dynamic system is the process of emergence, that is, the origination of novel, often surprising properties of the system as a whole that have causal properties exceeding those of the processes out of which they emerged. In Section 3.4.3, I shall discuss how emergence comes about as a result of process properties that govern complex dynamic systems such as art (Sections 3.4.2 and 3.4.3).
3.4.2 Cyclical Coupling
Some components will interact with some others, and in order to form a system, there must be a connecting path – through one or many of these interactions – from one component to any other one. The notion of connecting paths implies that complex systems are characterized by cyclical coupling or feedback loops (see Figure 3.5).
Take for instance the example of an art system where we distinguish the way works of art are created (component C), the way they are presented to a public (component P) and the way they are experienced by that public (component E).Footnote 64 In a linear dynamic system, the effect of one component onto another may run from C to P to E (see Figure 3.5). This is an example of an acyclic graph (a graph is a representation of a network in terms of nodes and arrows). If C, P, and E form a complex system (which, given Jones’ analysis of its recent history is highly likely), the relationship between the three must be cyclical, for instance, from C to P to E and back to C (see Figure 3.5). A feedback loop means that, for instance, creation of works of art affects the way works of art are experienced by a public and the way an audience experiences works of art affects the way works of art are created. An autofeedback loop means that a component has an effect on itself, for instance, the way a work of art is created affects the way a work of art is created (e.g., in the future). Autofeedback loops are iterative processes (the current state of art creation affects the next state, which is the current state for its next one, etc.). Cyclical coupling does not mean that everything is directly connected to everything else: a component of a system can be connected to another one through various intermediate connections.
Note that a system can be complex, even if it involves only few components. Around the turn of the twentieth century, the French mathematician Henri Poincaré showed that when as few as three celestial bodies interact according to strict deterministic Newtonian laws, their movements become chaotic, that is to say, unpredictable for all practical intents and purposes.Footnote 65 And a very simple, one-dimensional deterministic system governed by the discrete logistic equation produces totally erratic, surprising, and unpredictable behavior.Footnote 66 It is not the number of components per se that makes a system complex but the nature of their interactions.
3.4.3 Nonlinearity
Cyclical couplings and feedback loops give rise to nonlinear effects. Technically, nonlinearity means that the effects of separate components do not add up. In practice, this means that the effect of a component on another one is not proportional to the magnitude of that component (see, for instance, Tschacher and Tröndle’s analysis of the nonlinear effects of increasing or decreasing investments in the art marketFootnote 67). Nonlinearity is associated with temporal stability (e.g., in the form of the major epochs of art) as well as with the occurrence of tipping points and discontinuities, such as sudden changes in a particular artist’s style (e.g., Section 8.6). All depends on how the components in a system are connected with one another, how they interact: a complex system is governed by an interaction-dominant dynamics, rather than by the individual contribution of its many components (see also Section 5.1).
There are many more nonlinear properties that are due to the way complex systems interact: self-similarity, fractality, and criticality, which will be explained further in this book, in relation to properties of art systems.
3.4.4 Emergence, Self-organization, and Cyclical Causality
Through their interactions, the components undergo changes, resulting in emergent properties. Emergent propertiesFootnote 68 apply to the system as a whole and are not reducible to properties of the components (see the definition of a complex dynamic system in Section 3.4.1). Emergent properties are new: they are often highly surprising, creative results of the underlying processes. “New” does not mean unique: a young child’s emerging language is an entirely new capacity for this child, but billions of children have gone through a similar process of emergence. Emergence is thus related to creativity, and as such, creativity is a property of the universe as a whole, and much more general than human creativity. Emergent properties are the result of self-organization: in a complex system, the pattern of interactions is not driven by an external directive agent or building plan, it originates out of itself. Because of this possibility of self-organization of emerging, novel, and often unexpected properties, complex systems are predictable only to a limited extent. For instance, what Kubler calls reproductive sequences of art are highly predictable, whereas innovative “inventions” are not predictable at all (they are examples of emergent properties that are new, as well as unique).
Emergence is a universal phenomenon that applies to the most fundamental aspects of quantum physics to the phenomena of life and mind.Footnote 69 The levels of organization that form the focus of the sciences amount to forms of emergence: phenomena studied by chemistry are emergent properties of underlying atomic and quantum-physical interactions; biophysical and biochemical levels of organization emerge from interactions at the chemical level; the biology of interacting organisms emerges from underlying biophysical and biochemical processes; cognitive and mental phenomena emerge from underlying biological processes; and culture emerges from cognitive and mental phenomena.Footnote 70 All these levels of emergence are interconnected; they cannot be separated (there is no human culture, for instance, without underlying biological processes, but culture can enable as well as constrain biological processes). In Mind and Emergence, Philip Clayton describes emergence as “… the theory that cosmic evolution repeatedly includes unpredictable, irreducible, and novel appearances.”Footnote 71 Art is, no doubt, an emergent phenomenon of human material and social activity, generating unpredictable, irreducible, and novel appearances: works of art, styles, artforms, art experiences, and so on.
Self-organizing, emergent properties are attractors: that is, they remain stable and self-sustaining for a while. Depending on the nature of the underlying dynamics, they can transform themselves into new attractors, that is, new emergent patterns (a simple example is that of a succession of major epochs in the history of art, characterized by specific, relatively stable, stylistic principles).
A defining property of emergent properties, which originate from – and in this sense are caused by – the interactions between their underlying components, is that they have causal powers by themselves. These causal powers have at least two different forms. Let me explain this with an example.
The first of these causal forms implies cyclical causality. First, a work of art is an emergent pattern, with specific emerging properties, such as affordances for experience and creation of new works of art. It self-organizes out of many underlying components, in the first place the affordances presented by the materiality of creation. For a painter, this materiality entails canvases, or other supports, paints, workshop conditions, and so forth. For a contemporary artist, the possibilities concerning the materiality of the support have become virtually infinite, ranging from objects and spaces to film to digital worlds. Second, a work of art self-organizes in the activities of its creation, such as preliminary thoughts and ideas, drawings, sketches, corrections, material actions such as brushstrokes, and so forth. As these activities proceed, the work of art gradually emerges as a specific, self-sustaining pattern (e.g., a pattern of colors on a canvas that is more than the sum of the individual color patches). During its creation, the emergent work of art constrains and enables the ongoing activities of creation, by offering adjacent possibilities of action that become more and more constrained as the work of art reaches its finalization. That is, emergence and the underlying activities present a pattern of cyclical causality,Footnote 72 or cyclical conditionality: the underlying activities are the cause of the emergent artistic pattern, and the emergent artistic pattern is the cause of the underlying activities (see Figure 3.6).
Figure 3.6 The structure of cyclical loops between lower-level and higher-level (emergent) processes; in this example, lower-level processes are micro-activities during the creation of a work of art; the higher-level process is that of an emergent artistic form (e.g., a painting, sculpture, installation, taking shape across the process of creation…).
Cyclical causality is possible if the processes are extended in time, if causality proceeds in sequences of events,Footnote 73 that is, sequences of activities of creation or of interpretation.
For instance, the brushstrokes of a contemporary painter or the experiencing of a work of art by a viewer reflect the current condition of the artworld in which this artist or viewer are embedded, and all micro-activities of artists, viewers, dealers, and critics constrain and enable the long-term change of styles, ideas, philosophies, and the body of artistic work that characterize the artworld in its current state. We just saw that a work of art emerges from its underlying processes of drawing, sketching, designing, painting, constructing, and that the underlying processes themselves are constrained, enabled, and determined by the emerging work of art. This reciprocity is described by Rudolf Arnheim, in his study of Picasso’s creating Guernica, or in Goldschmidt’s study of the short-term process of sketching and its relation to the long(er)-term timescale of the emergence of an architectural form.Footnote 74 The processes of prestigious gallery display of works of art create the unique artistic and associated economic value of those works of art, and the participation of artistic celebrities and exceptionally expensive works of art create the prestige of the galleries showing them.Footnote 75
The second type of causal power implies that emergent patterns or properties are causally or conditionally related to other emergent patterns and other processes of emergence. For instance, a particular work of art – which emerges from the activities of creation – may serve as the starting point for other works of art, and lead to continuous reproductive series, or to discontinuities in the form of sudden innovations (see Kubler’s ideas on such series discussed earlier, or Gell’s idea of the artist’s oeuvre as a distributed dynamic objectFootnote 76).
We have seen that the state of a complex system and the way it changes over time can be represented in a state space consisting of descriptive dimensions. The problem with a state space representation is that the dimensions are fixed, that is, there is no room for emergence and novelty, as emergence implies that a new and unexpected property originates from the complex system. This new feature requires an additional state space dimension, which, if the emergent property is really novel, cannot be foreseen in advance. For instance, it is unlikely that the self-reflective shift in the visual arts that took place at the beginning of the twentieth century, with the work of Marcel Duchamp for instance, could have been foreseen by a nineteenth-century art theorist. Hence, creativity – which implies emergence – is only possible if the state space itself is dynamic, that is, continuously reshaping and expanding, adding new dimensions.Footnote 77
Although emergent properties in the form of innovations and creativity cannot be predicted, the distribution with which innovations occur on the long-term timescale follows strict statistical laws, known under a variety of terms: Zipf’s law, Heap’s Law, Taylor’s law. These laws state that the probability of finding an innovation of magnitude x (assuming we can express innovations in terms of how novel they are) is proportional to a fraction, namely 1 divided by x raised to some power (e.g., 2, 1.3, …). This type of law is remarkably robust and appears everywhere in complex dynamic systems, from earthquakes to creative innovations.Footnote 78 In Chapters 9 to 13, I will give many examples of how this law applies to art.
3.4.5 Idiosyncrasy and Non-ergodicity
The problem is that networks of dynamic relationships consist of a vast number of components, of many different kinds – some associated with the person, activity, and skill of the artist and others associated with the social, cultural, and commercial context. In addition, these networks are in all likelihood highly idiosyncratic; they are person- or artist-specific. The composition of these networks and the processes that characterize them are likely to change over the course of time, dependent on the timescale at which the processes of interest occur. It is virtually impossible to determine the contribution of each of these components separately, for instance how a particular component contributes to an artist’s significance or success. The idea that each component of a network has its own specific, separate effect is based on the assumption that such networks are linear systems, that is, it is assumed that the resulting dynamics are component-dominant. In a component-dominant dynamics, processes result from the addition of the effects of a number of independent components or factors. Any replacement of a component by another, or any significant change in a component (for instance, a change in the expressive function), has a direct and proportional consequence on the outcome of the dynamics. If a lot of individual processes are lumped together, that is, if the specific dynamics of individual processes are discarded and only group trends and averages are focused on, the resulting dynamics can be analyzed as a component-dominant dynamics of general trends. However, models of general trends are mostly not applicable to real processes, as real processes always occur in specific contexts, and are to a large extent idiosyncratic (individually specific). This incompatibility between general trend models based on populations (e.g., populations of nineteenth-century artists) and real processes is currently known as the ergodicity problemFootnote 79 (Sections 8.3 and 13.4).
To understand the principle of component-dominance, imagine the changing profits of a particular investor who has several portfolios. Each portfolio is a component in the investor’s total profit. Every component goes up and down dependent on the stock market. The biggest portfolio makes on average also the biggest contribution to the investor’s profits or losses. Hence, the profit–loss dynamics is clearly dominated by the addition of distinct components (portfolios).
However, the stock market itself is an interaction-dominantFootnote 80 dynamics, that is to say, it is the nature of the typical interactions of the stock market system that explains its short- and long-term behavior. It consists of a great number of components on various levels of organization, for instance stockbrokers and traders, investors, and companies represented by stocks or shares, bonds, and securities. These components form a network of complex interactions and feedback loops. The interactions and feedback loops occur on various levels of organization and their corresponding timescales, ranging from the short-term events of actual buying and selling, including all the emotional and cognitive processes occurring during a stockbroker’s buying or selling a bond, to the long-range evolution of stock prices and markets. Hence, the stock market is the result of its interaction dynamics, and not a sum of separate contributions.Footnote 81
Artworlds are not stock markets, but they share an important feature with the latter, and with all sorts of complex dynamic systems for that matter, namely that their dynamics are interaction-dominant, which means that “… they exhibit nonlinear feedback among the interactions of their parts, such that it is the continual interactions of the parts that facilitate the system level dynamics.”Footnote 82 Interaction-dominant dynamics give rise to characteristic features of complex dynamical systems, namely emergence, self-organization, and nonlinear effects, which will be illustrated in the following chapters.
3.4.6 Complex Dynamic Systems as Models for Art
If something, art for instance, complies with the basic definition of a complex dynamic system, namely that it is a network of many interacting components that change as a result of their interactions; it will also have the properties that are characteristic of complex systems in general. That is, we can expect that processes of art will show self-organization, emergence, attractors of various kinds, and nonlinearity. In Chapter 4, I will focus on a description of the visual arts through the lens of complex dynamic systems.
