Interactive Organic Art

** **

*Department of
Electrical Engineering and Computer Science, University College London, London,
England.*

*e-mail:
r.behravan@ee.ucl.ac.uk*

* *

*Glassworks Ltd.
Visual effects and post production, London, England.*

*e-mail:
robin@glassworks.co.uk*

** **

** **

Abstract

In this paper we explore the use of sound to interact with the
artificial biological patterns based on reaction-diffusion systems. Modelled by relatively straightforward cellular
automaton, reaction-diffusion systems can seem alive and interaction with such
systems through touch, sound and music creates an organic, fluid and
non-repeatable aesthetic experience.

The aim of our system is to use reaction-diffusion to create an
aesthetic accompaniment to music, for use in applications such as art
installations and music venues. With an appropriate mapping from music to
reaction-diffusion, we aim to translate some of the emotional content of sound
into visuals, enabling an investigation of how changing patterns in different
media affect us emotionally.

In
his paper “*chemical basis of morphogenesis*”, Alan Turing devised a
system to model biological development and pattern formation [9]. *Reaction-diffusion*
systems are based on the communication amongst cells by the way of chemicals.
It is an attempt to explain symmetry breaking and pattern formation in the
early embryo, generating growth. These
mathematical systems can be utilised to generate two-dimensional organic
patterns resembling stripes on zebra skin or spotty patterns seen on fish skin.

In
this article we will describe the science of reaction-diffusion while exploring
the aesthetic values of interacting with such systems using sound and touch.
However the beauty of reaction-diffusion systems should not let us forget the
importance of the fundamental biological questions that they might be able to
answer.

In the first part of this article we will explain the background and the tools we need to implement our system. We then explain the system and its method of visualization. In the last section of this article we will discuss the motivation behind the usage of science and mathematics in creating art.

2.1 Reaction-Diffusion and Pattern Formation

**2.1.1 Biological Development.**
How does a highly organized body plan emerge from a single cell? This is one of
the most fundamental questions in developmental biology. Development is the
emergence of organized structures from an initially simple group of cells [4].
In 1952 Alan Turing proposed a hypothetical chemical reaction that could
spontaneously break the symmetry in an initially uniform mixture of chemical
compounds, leading to stable spatial patterns [9]. He was hoping that this
would provide a model for how patterning takes place in an initially
homogeneous fertilized egg. He called these chemicals *morphogens* –
intending to convey the idea of form producers [8].

**2.1.2 ****Reaction-Diffusion. **Reaction-Diffusion systems are pattern generating,
self-organizing complex systems that hope to model the initial stages of
biological development. These systems are based on cell communication by the
way of interaction of two or more chemicals.

*Diffusion
*is the action of spreading of
morphogens and *Reaction* is the process that creates and destroys
morphogens, based on their concentration in each cell [10]. In Turing’s
chemical system, diffusion is competing with autocatalytic and inhibitory
chemical reactions [5].

**2.1.3 ****Mathematical Model. **Reaction-diffusion systems are modelled by the
partial differential equations where the rate of change of each chemical
depends on some function of reaction plus some function of diffusion.

da/dt = F(a,b) + D_{a}Ñ^{2 }a

db/dt = G(a,b) + D_{b}Ñ^{2}b

Where
da/dt and db/dt describe the rate of change
of chemicals *a *and *b*, with respect to time. The Laplacian
operator applied to *a* or Ñ^{2}*a* is
the measure of how high the concentration of *a* is at one location with
respect to the concentration of *a *nearby (its neighbours). Ñ^{2}*b* is the measure of how high the
concentration of *b* is at one location with respect to the concentration
of a nearby *b*. D_{a} and D_{b} represent the diffusion
rate of chemicals *a* and *b* and F(a,b) and G(a,b) are some reaction
function of chemicals *a* and *b*.

Although Turing
was the pioneer of this discipline, others have devised other
reaction-diffusion systems, the most important of which are the Meinhardt and
the Gray-Scott systems. The three equation systems are provided below:

**Turing Equations.**

da/dt = D_{a}Ñ^{2 }a + s (16 – ab)

db/dt = D_{b}Ñ^{2}b + s (ab – b –b)

Where the
parameter *s* is the reaction speed and b is the source of slight random
irregularities in chemical concentration [9].

**Meinhardt Equations.**

da/dt = D_{a}Ñ^{2 }a + s (a^{2} / b + b_{a})
– r_{a}a_{}

db/dt = D_{b}Ñ^{2}b + sa^{2} + b_{b }- r_{b}b

Where
the parameters b_{a }and* _{ }*b

**Gray-Scott Equations. **

da/dt = D_{a}Ñ^{2 }a – ab^{2 } + F(1 – a)

db/dt = D_{b}Ñ^{2}b + ab^{2 } + b(F + K)

Where the parameter *K* is
the dimensionless decay rate of the reaction and *F* represents the rate
of the process [7].

Analytical
solutions for differential equations are not always possible and that is why we
seek discrete numerical techniques.

2.2 Cellular Automata

A**
**Cellular automata is a one, two or three-dimensional grid of cells in which
the fate of a cell or its rate of change with respect to time is determined by
the states of its neighbours through a set of local rules. Cellular automata
provide simple and discrete mathematical models and can act as good models for
biological and physical phenomenon [2].

To
model reaction-diffusion systems using two-dimensional cellular automata, each
cell starts with a certain amount of chemicals *a* and *b*. The
Laplacian Ñ^{2}*a* refers to how much of a chemical a cell contains
compared to its neighbours. By neighbours we mean cells on the top, bottom,
left and right.

*Figure 1 represents a small section in a **cellular
automata. *

*The cell in the middle contains a
certain amount of chemical a represented by x*a and a certain amount of
chemical b, y*b. *

*The arrows represent the **neighbouring** cells.*

*Fig. 1*

*This
is to provide the information for the update of the chemical amount in a cell
relative to its neighbours. The value of the reaction function is then
calculated which depends on the amount of chemicals a and b in that cell. The
amount of chemicals a* *and* *b*
*in all cells can then be updated simultaneously by evaluating and adding*
da/dt
*and* db/dt *to the amount of a and b in each cell using any of
the above equations.*

2.3 Visualisation

An example of
how to visualise such a system using computer graphics, is to create an
imaginary grid of cells, each of which would contain a certain amount of
chemicals. Each chemical would be specified its own colour. A pixel would
represent a cell whose colour is the combination of the colours of the
chemicals in that cell.

2.4 Interaction

The mathematical equations of Turing, Meinhardt and Gray-Scott can be manipulated to create different results or patterns by varying the values of parameters. For example the size of the spots created by the Turing equations are dependent on the value of s, the larger the value of s, the smaller the spots. Figures 2 and 3 have been generated using the Turing equations. S has a larger value in Figure 2 than it has in figure 3.

*Fig. 2*** ** *Fig. 3*

In
the Gray-Scott equations by varying the amount of *k*, we can turn spots
to stripes and vice versa. Figures 4 and 5 were generated using the Gray-Scott
equations; K has a larger value in Figure 5 than it has in figure 4.

By allowing the change in the value of a parameter, for example the size of the spots, to correlate with the change of another variable, for example the volume level of a piece of music or a human voice, we can create interactive audio-visuals.

2.5 Sound

Sound is a wave
which is created by vibrating objects and propagated through a medium from one
location to another. The simplest kind of pressure wave is a sine wave. Figure
6 shows the air pressure against time or the sound wave of 1/20 seconds of a
piece of music.

*Fig. 6*

Fourier transform is based on the idea that any wave can be expressed as a
sum of sine and cosine waves. Using
Fourier transform, we can decompose a signal or a (sound) wave to its component
frequencies. Figure 7 represents the graph of frequency against amplitude of
the same 1/20 seconds, represented in figure 7.

*Fig. 7*

The decomposition
of sound will allow us to manipulate parameters in reaction-diffusion systems
by relating them to the subunits of sound. This will also allow us to change
the colour of the visuals we are creating according to the frequencies of
sound, representing interaction.

2.4 Generative Art

In
this work we use the definition of generative art proposed by Philip Galanter:

“Generative art
refers to any art practice where the artist uses a system, such as a set of
natural language rules, a
computer program, a machine, or other procedural invention, which is set into
motion with some degree of autonomy contributing to or resulting in a completed
work of art.” [3]

Generative art
can be used as a method for developing ideas and as an aid to human creativity.
This is an area of art in which the outcome is unpredictable. Moreover the end
or the final result is not necessarily an issue, unlike other areas of art. We
will now review a few generative artists and their work.

**Mauro
Annunziato** is a scientist and also
an artist working in the area of artificial life and the application of
complexity to art. He uses chaotic, self-organizing and complex systems
together with genetic algorithms to create interactive audio-visual
installations.

**Philip
Galanter** creates various kinds of
generative software and hardware systems. In his most relevant work to this
article, *self-organized drawing*, he uses reaction-diffusion systems to
generate the macrostructure and then uses genetically based software for the
generation of the microstructure of the drawings [3].

** **

**Daniel
Bisig** has created a sound
interactive growth art installation called *BioSonics,* which transforms
the user sound interactions, into spatial and temporal patterns. In this
system, sound is converted into chemicals, which cause the dynamics in the
chemical reactions to change leading to the growth processes [1].

**David
Fried** has created a series of
interactive sound-stimulated sculptures called self-organising still life in
which solid spheres interact with one another and are also stirred into motion
by ambient sound[1].

The tools we
need to implement our system are two-dimensional cellular automata for
generating two-dimensional patterns, a suitable reaction-diffusion system and a
suitable way of interacting with sound.

* *

**Reaction-diffusion
system.** In our experiments with all three systems of reaction-diffusion,
we came to the conclusion that the Gray-Scott equations are the most
appropriate for real-time interactivity. This is because in the Turing and
Meinhardt systems, we start with a grid of cells in a cellular automata, all of
which are then allocated the same amount of chemicals *a* and *b*
plus a certain amount of randomness in the chemicals. Then using the equations,
the amount of chemicals in each cell is updated, and in doing so, a process of
self-organisation and refinement begins and patterns start to emerge. Turing
and Meinhardt systems converge to a solution, a final result, whereas the
Gray-Scott equations, with the right parameters can be highly dynamic and
unpredictable and create non-repeatable non-stopping patterns.

In
the Gray-Scott system, all the cells are initialised with no amount of
chemicals and then a small amount of perturbation is introduced to a small area
of the grid. Using the mathematical equations to update the amount of chemicals
in each cell, the area of small perturbation begins to grow in a fluid, life
like manner. This fluidity allows the sensation of interaction by touch or a
mouse in the way of changing the amount of chemical in the cells that are
touched with a mouse. Also the speed of changing from one pattern to another
allows the interaction with touch or a mouse or sound using Gray-Scott
equations, very effective.

Another
reason to use the Gray-Scott equations is the range of value for certain
parameters which make the system very chaotic, creating volatile patterns
generated by the birth and annihilation of patterns. This volatility of the
system will allow us to create never-ending visuals. This non-stability is not chaotic enough to seem random and is
not ordered enough to seem uninteresting. It is somehow unpredictable but
always familiar; similar to fire, clouds and lava lamps. It reminds us of the
idea of the edge of chaos, an interesting area complexity theory where
interesting solutions exist.

** **

**Visualisation. **The
two-dimensional cellular automata that we used for our experiments can be
represented as a set of cells or points flat on a two-dimensional grid or they
can be mapped on to a three-dimensional surface a sphere for example.

In computer
graphics many three-dimensional models are represented using polygons. If we
think of the surface of a any three-dimensional computer model as a set of
points each of which having a certain amount of some chemicals represented by
some colours, we can run reaction-diffusion systems onto any kind of surface
and not just a flat two-dimensional model.

For
our purposes we use three-dimensional models created with triangles like the
sphere shown in figure 8. Figure 9 shows the use Gray-Scott equations on the
geodesic sphere.

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*Fig.8* *Fig. 9 *** **

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**Sound Interaction**. Our system combines two-dimensional cellular automata modelling reaction-diffusion, synchronised by the real-time fluctuations of audio volume
input to the system. Frequency (pitch) derived from Fourier transform is used
to determine colour of emerging
patterns. In some of our experiments we have allocated reddish colours for deeper sounds and bluish colours for higher frequencies. Also the size of the
patterns change according to frequency and volume, smaller patterns for higher
frequencies and volume and larger patterns for lower frequencies and volume.
This method can loosely be used to reflect ones mood by the changing colours and patterns according to the volume and the
frequency of ones voice. User interaction (keyboard and mouse) enables
reaction-diffusion parameters to be altered, causing a user-determined “flow”
of patterns.

By decomposing the sound wave in to its component frequencies using a Fourier transform, we basically create many waves, each of which can be linked to a parameter in a mathematical system for example a reaction-diffusion to vary the value of that parameter. Moreover the range of the value for a parameter in a reaction-diffusion system can be changed according to the range of the volume of the sound of interaction.

The
main aim of this article was to introduce the basic ideas and methods for
generating organic visuals using computer graphics and also an introduction to
use of sound for interaction with any multi-parameter system. It is important
to realise the importance of mathematics and science in creating systems such
as the ones described in this paper. Also it is important to note that
mathematics can be used not just for abstracting scientific concepts but as a
tool for creation of art. Moreover none of this work would have been possible
without the use of computers and computer graphics. We live in a very exciting
time of digital revolution where we can put most ideas in to the practice using
computers.

None
of our artwork has been shown in this paper. For the purposes of this article,
we intended to introduce the reader to the tools and to encourage them to use
their own creativity and imagination to create their own interactive computer
art. However the interested reader will be able to see our artwork on the
following website * **http://www.hoohar.com/ramona/ .*

1 ) Bisig, D., 2003. BioSonics
– Interactive Growth System. In proceedings
of the sixth Generative Arts
Conference. Milan: Italy.

2 ) Camazine, S.,
Deneubourg J. L., Franks N. R., Sneyd J., Theraulaz G., Bonabeau E., 2003. *Self-Organization
in Biological Systems*, New Jersey: Princeton University Press.

3 )
Galanter, P., 2003. What is Generative Art? Complexity Theory as a Context for Art Theory. Interactive
Growth System. In proceedings of the sixth
Generative Arts Conference. Milan: Italy.

4 ) Lewis, W., 2002. *Principles
of Development*, New York: Oxford University Press.

5 ) Meinhardt, H., 1982.
Models of biological pattern formation, Germany: Academic Press.

6
) Meinhardt, H., 1995. *Algorithmic beauty of sea shells*,
Germany: Springer, third edition.

7 ) Pearson, J. E., July
1993. Complex patterns in a simple system, Science, 261,189.

8 ) Saunders P. T., 1992.
*Collected works of A..M Turing*: *Morphogenesis. *Amsterdam,
Holland:* *North Holland.

9 ) Turing, A.M., 1952.
The chemical basis of morphogenesis. Philosophical Transactions of the Royal
Society London: B327, 37-72.

10 ) Turk, G., July 1991. Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion. In proceedings of SIGGRAPH conference, Computer Graphics, Vol. 25, No. 4, pp. 289-298.