=Paper=
{{Paper
|id=Vol-1520/paper15
|storemode=property
|title=Creative Systems as Dynamical Systems
|pdfUrl=https://ceur-ws.org/Vol-1520/paper15.pdf
|volume=Vol-1520
|dblpUrl=https://dblp.org/rec/conf/iccbr/Valitutti15
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==Creative Systems as Dynamical Systems==
https://ceur-ws.org/Vol-1520/paper15.pdf
146
Creative Systems as Dynamical Systems
Alessandro Valitutti
School of Computer Science and Informatics, University College Dublin,
Belfield, Dublin D4, Ireland
alessandro.valitutti@ucd.ie
Abstract. In this paper, we discuss ideas for characterizing a case-
based generative system as “creative”. Focusing on a specific generator
of graphics, we performed a qualitative exploration of the space of solu-
tions. The emerged intuition is that the set of configurations 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.
1 Introduction
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 [1].
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 different initialization of the parameters should
allow the system to produce different 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 sys-
tems introduced by Boden [2], formalized by Wiggins [12] and further extended
by Ritchie [11]. In this context, the case-based adaptive process can be viewed
as a type of exploratory creativity, i.e. a search in the space of artifacts or con-
ceptual space, where the set of past examples are the inspiring set. Ideally, the
output of the search should be an artifact provided with a form of value and
expressing the balance between familiarity and novelty described by Giora as
optimal innovation [4].
Focusing on a specific generator of graphics, we performed a qualitative ex-
ploration of its generative parameters, described in the next section. The rest of
the paper discusses the insights inspired by this example.
Copyright © 2015 for this paper by its authors. Copying permitted for private and
academic purposes. In Proceedings of the ICCBR 2015 Workshops. Frankfurt, Germany.
147
2 Exploring the Space of Fractal Trees
We focused on an algorithm for the visual representation of a fractal tree, a
fractal geometrical shape defined by recursion as follows: (1) Draw a trunk;
(2) At the end of the trunk, split by some angle and draw a prefixed number of
branches; (3) Repeat at the end of each branch until a sufficient level of branching
is reached1 . The original code of the program2 was implemented in Processing
programming language [10]. For the mathematical details, we refer the reader
to Mandelbrot’s treatment [8, pp.151-161]. The shape depends on the value
of two parameters representing the angle between two adjacent branches and
the rotation angle performed on both of them, respectively. Their values are
associated to the two coordinates of the mouse cursor in the output window.
In this way, moving the cursor in different points of the screen, it is possible to
generate an unlimited number of configurations.
In order to show the set of possible configurations in a small portion of the
output window, we modified the code in such a way to draw a small square and
to map the configurations to the coordinates of its internal points.
Fig. 1. Examples of configurations generated by the position of the cursor in different
regions of the conceptual space mapped in the square.
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.
148
Curvature Aperture Symmetry
Fig. 2. Configurations according to different dimensions.
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 de-
scribed by Douglas Hofstadter in what he called an “exotic trip”. He put his
description in “Gödel, Escher, Bach” [5, pp.483-488] as a fictional 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 observa-
tions.
Shape Types Our first finding was that there are regions in the square cor-
responding to different types of shapes. As shown in Figure 1, some regions gen-
erate shapes recognizable as vegetable forms such as stone pines, firs, broccoli, or
roots. Other regions generate polygons such as triangles, rectangles, or polygon
spirals. Finally, there are regions associated to more complex shapes resembling
snowflakes. Each region seems to correspond to specific “natural concept”, as
defined by Gärdenfors [3].
Shape Dimensions The second observation is that, in each region, the
shapes can be associated to a number of perceptual dimensions ascribable to
Gärdenfors’ “quality dimensions”. Specifically, we identified three dimensions:
curvature, aperture, and symmetry. Each dimension seems to identify a specific
149
trajectory in the conceptual space. Figure 2 shows some configurations accord-
ing to the observed dimensions. Curvature and aperture can be easily defined in
terms of the generative parameters. For example, since the overall figure is the
superposition of a fixed number of broken lines, curvature can be defined as the
angle formed by two adjacent segments in the broken line. According to the first
column of Figure 2, the trajectory of curvature is a horizontal line. Moreover,
aperture can be defined as the average difference between the curvature of two
adjacent components. In the case of symmetry, the definition in terms of gener-
ative parameters seems more naturally definable “a posteriori”, as a constraint
on the generated shape.
Optimal Configurations Finally, the third observation is that, in each
region associated to specific type of shapes, the aesthetic value of the shapes
seems to change according to different generative parameters and dimensions.
Furthermore, each column of Figure 2 shows that the aesthetic value seems to
reach a maximum in correspondence of specific subsets of each region. These
“optimal configurations” seem to be associated to specific 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 definition 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 different shapes. Specifically, we intend to employ type
of evaluation with subjects analogous to the one performed by Noy et al. [7]
3 Basin Jumping
If we consider a specific 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 configurations, we can view it from two different
perspectives. On one hand, the path can describe a search session in the con-
ceptual 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
different shape types, as basins of attraction and their optimal configurations 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 [9]. We go beyond the specific example described above and suppose
that there is a large number of creative systems whose conceptual spaces can be
decomposed in basins of attraction. Moreover, we hypothesize that the “creativ-
ity” of these system should not simply consist of the capability to generate the
conceptual space and, starting from an initial configuration, explore its basin of
attraction. Indeed, they should be capable of reaching basins of attraction not
containing the past examples. In other words, if we assume the creativity as a
search in the conceptual space, a higher degree of creativity is associated to the
search of new basins of attraction.
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4 Learning to Jump
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
different 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 definitions of perceptual dimensions and
aesthetic value. A crucial aspect is the combination of two types of heuristics,
the first one for the discovery of new basin of attraction, and the second one for
the identification of the optimal configuration.
Acknowledgments This research was supported by the EC project WHIM:
The What-If Machine. See http://www.whim-project.eu.
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