In this paper, we discuss ideas for characterizing a casebased generative system as \creative". Focusing on a speci c generator of graphics, we performed a qualitative exploration of the space of solutions. The emerged intuition is that the set of con gurations generated by the program can be viewed both as the conceptual space of a creative system and the phase space of a dynamical system. In the context of this analogy, we hypothesize that a higher degree of creativity can be ascribed to the search paths allowing the system to reach new basins of attractions.
Case-based reasoning (CBR) is a type of problem solving in which a new solution
is found through the retrieval of a similar available case and the adaptation of
the related solution [
Let us suppose to have a computer program for the generation of artworks such as graphics, musical pieces, or poems, and a set of generative parameters. Given a set of known examples, a di erent initialization of the parameters should allow the system to produce di erent corresponding instances of the same type of artifact. However, the production of new artifacts does not necessarily imply that they would be recognized as original and valuable. In this paper, we discuss ideas for characterizing the re-use of past solutions, performed by a case-based generative system, as \creative".
An artwork generator can be framed in the context of ideas on creative
systems introduced by Boden [
Focusing on a speci c generator of graphics, we performed a qualitative exploration of its generative parameters, described in the next section. The rest of the paper discusses the insights inspired by this example.
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We focused on an algorithm for the visual representation of a fractal tree, a
fractal geometrical shape de ned by recursion as follows: (1) Draw a trunk;
(2) At the end of the trunk, split by some angle and draw a pre xed number of
branches; (3) Repeat at the end of each branch until a su cient level of branching
is reached1. The original code of the program2 was implemented in Processing
programming language [
In order to show the set of possible con gurations in a small portion of the output window, we modi ed the code in such a way to draw a small square and to map the con gurations to the coordinates of its internal points. 1 This version of the algorithm description is reported on http://rosettacode.org/ wiki/Fractal_tree 2 The code of the original program is available at http://www.openprocessing.org/ sketch/5631. Curvature
Aperture
Symmetry
We observed the changes of the shape while moving the mouse cursor over the square. In doing that, we were inspired from a qualitative exploration described by Douglas Hofstadter in what he called an \exotic trip". He put his description in \Godel, Escher, Bach" [5, pp.483-488] as a ctional dialogue and, three decades later, as a more detailed report [6, pp.65-69]. Hofstadter used a video camera pointed in various ways toward the output screen, and capable of generating several possible patterns. In particular, we made three main observations.
Shape Types Our rst nding was that there are regions in the square
corresponding to di erent types of shapes. As shown in Figure 1, some regions
generate shapes recognizable as vegetable forms such as stone pines, rs, broccoli, or
roots. Other regions generate polygons such as triangles, rectangles, or polygon
spirals. Finally, there are regions associated to more complex shapes resembling
snow akes. Each region seems to correspond to speci c \natural concept", as
de ned by Gardenfors [
Shape Dimensions The second observation is that, in each region, the shapes can be associated to a number of perceptual dimensions ascribable to Gardenfors' \quality dimensions". Speci cally, we identi ed three dimensions: curvature, aperture, and symmetry. Each dimension seems to identify a speci c trajectory in the conceptual space. Figure 2 shows some con gurations according to the observed dimensions. Curvature and aperture can be easily de ned in terms of the generative parameters. For example, since the overall gure is the superposition of a xed number of broken lines, curvature can be de ned as the angle formed by two adjacent segments in the broken line. According to the rst column of Figure 2, the trajectory of curvature is a horizontal line. Moreover, aperture can be de ned as the average di erence between the curvature of two adjacent components. In the case of symmetry, the de nition in terms of generative parameters seems more naturally de nable \a posteriori", as a constraint on the generated shape.
Optimal Con gurations Finally, the third observation is that, in each
region associated to speci c type of shapes, the aesthetic value of the shapes
seems to change according to di erent generative parameters and dimensions.
Furthermore, each column of Figure 2 shows that the aesthetic value seems to
reach a maximum in correspondence of speci c subsets of each region. These
\optimal con gurations" seem to be associated to speci c ranges of curvature,
aperture, and symmetry. At this stage of the research, this claim is proposed as
an intuition to be formalized and empirically evaluated. In particular, it would
be necessary to attempt a formal de nition of aesthetic value in terms of the
shape dimensions mentioned above. Moreover, an evaluation with human judges
is needed to study to what extent there is agreement on the aesthetic values and
their variation along the di erent shapes. Speci cally, we intend to employ type
of evaluation with subjects analogous to the one performed by Noy et al. [
If we consider a speci c path in the square mapping the conceptual space, such
that the variation of the aesthetic value is positive and reach its maximum in
correspondence of the optimal con gurations, we can view it from two di erent
perspectives. On one hand, the path can describe a search session in the
conceptual space of a creative system. On the other hand, it can be interpreted as
a trajectory in the phase space of a dynamical system. According to the second
interpretation, we can view each region of the conceptual space, associated to
di erent shape types, as basins of attraction and their optimal con gurations as
the corresponding attractors. An attractor is a set of states (i.e., elements of the
state space of a dynamical system) towards which a set of dynamical paths tend
to evolve [
The intuitions proposed in this work are aimed to identify a possible limitation in the use of CBR as a creative tool and to overcome it. A creative CBR system should get a the description of an artifact (i.e. an element of the conceptual space) as input case and retrieve one or more similar cases and reuse the corresponding knowledge to generate them. A possible intrinsic limitation is the use of similarity of past solutions. In terms of dynamical systems, we believe that this approach constraints the search inside a single basin of attraction. The suggestion emerged from the example described above is to identify perceptual dimensions and, through them, evaluation functions capable of reaching the maximum value in di erent basins of attractions.
In our next work, we aim to formalize, implement and empirically evaluate this approach. In particular, we intend to focus on generative systems analogous to the fractal tree generator and provide de nitions of perceptual dimensions and aesthetic value. A crucial aspect is the combination of two types of heuristics, the rst one for the discovery of new basin of attraction, and the second one for the identi cation of the optimal con guration.
Acknowledgments This research was supported by the EC project WHIM: The What-If Machine. See http://www.whim-project.eu.