Pherogenic Drawings

Generating Colored 2-dimensional Abstract Representations of Sleep EEG with the

KANTS Algorithm

Carlos M. Fernandes, Antonio Mora and Juan Julián Merelo

Department of Computer Architecture and Technology, University of Granada, Granada, Spain

Agostinho C. Rosa

Department of Electrotechnics, Technical University of Lisbon, Lisbon, Portugal

Keywords: Swarm Art, Generative Art, Ant Algorithms, Stigmergy, Pherogenic Drawings.

Abstract: Social insects and stigmergy have been inspiring several significant artworks and artistic concepts that

question the borders and nature of creativity. Such artworks, which are usually based on emergent properties

of autonomous systems and go beyond a centralized human authorship, are a part of a contemporary trend

known as generative art. This paper addresses generative art and presents a set of images generated by an

ant-based clustering algorithm that uses data samples as artificial ants. These ants interact via the

environment and generate abstract paintings. The algorithm, called KANTS, consists in a simple set of

equations that model the local behavior of the ants (data samples) in a way that, when travelling on a

heterogeneous 2-dimensional lattice of vectors, they tend to form clusters according to the class of each

sample. The algorithm was previously proposed for clustering and classification. In this paper, KANTS is

used outside a purely scientific framework and it is applied to data extracted from sleep-

Electroencephalogram (EEG) signals. With such data sets, the lattice vectors have three variables, which are

used for generating the RGB values of a colored image. Therefore, from the actions of the swarm on the

environment, we get 2-dimensional colored abstract sketches of human sleep. We call these images

pherogenic drawings, since the data used for creating the images are actually the pheromone maps of the ant

algorithm. As a creative tool, the method is contextualized within the swarm art field.

1 INTRODUCTION

Generative art is a contemporary trend that uses

autonomous systems for generating artworks or

ornamental objects. There may be more or less

human interaction with the process, but, in general,

the core of a generative artwork is the result of a

computational and sometimes emergent procedure.

Swarm Intelligence (SI) (Bonabeau et al., 1999) is

one of the techniques used in this field, whether as

computational simulations for creating digital art

that can be later translated to a physical medium, or

as guiding rules for groups of agents (robots, for

instance) that act directly (i.e., physically) on a

canvas. Within SI, social insects and the concept of

stigmergy have inspired significant artworks that

question the borders and nature of creativity. This

paper focuses on a digital approach and describes a

SI algorithm called KohonAnts (or simply KANTS),

used here for generating 2-dimensional non-

figurative images of correlated data sets of human

sleep.

KANTS is an ant-based algorithm proposed by

Mora et al. (2008) for data clustering and

classification. The method is loosely inspired by

Chialvo and Millonas’ Ant System (AS) (Chialvo

and Millonas, 1995), which is modeled by a set

equations and parameters that, when properly tuned,

guide the swarm to a self-organized state in which

complex patterns of global behavior emerge. Instead

of the 2-dimensional homogeneous lattice used in

(Chialvo and Milonas, 1995) as a habitat for the

swarm, KANTS evolve on a 2-dimensional lattice

with one vector of real-valued variables mapped to

each cell. The agents also differ from Chialvo and

M. Fernandes C., Mora A., Merelo J. and C. Rosa A..

Pherogenic Drawings - Generating Colored 2-dimensional Abstract Representations of Sleep EEG with the KANTS Algorithm.

DOI: 10.5220/0004158800720080

In Proceedings of the 4th International Joint Conference on Computational Intelligence (ECTA-2012), pages 72-80

ISBN: 978-989-8565-33-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Millonas model, since KANTS uses data samples

(with the same size as the environmental vectors) of

different classes as artificial ants. These ants travel

trough the grid, changing the values of the variables

so that they tend to be closer to their own values. At

the same time, the ants are attracted to the sections

of the habitat where the Euclidean distance between

the ant’s vector and the sections’ vectors is

minimized, i.e, the ants communicate via the

environment, an ability that is a fundamental part of

a process known as stigmergy (Grassé, 1959):

communication via the environment, with

modification of that same environment. The model’s

simple set of rules leads to a global behavior in

which clusters of ants/samples belonging to the same

class tend to emerge.

As stated above, the ants act upon the

environmental lattice, changing the vectors’ values.

Therefore, this array of vectors acts as a kind of

pheromone map that is shaped by the ants. The maps

are used in this paper for generating 2-dimensional

RGB colored images. The vectors’ values are

directly translated into the R, G, and B values (three-

variable sleep data set with is used here). Since the

ants tend to cluster, thus changing the values in that

region, it is expected that the pheromone map, after

a certain number of iterations, shows non-random

patterns, like a kind of a fuzzy patchwork. In

addition, the stochastic nature of the process and the

size and range of the data samples, make these sleep

signatures unique, not only for each patient, but also

for each night’s sleep. We believe that these

pherogenic drawings not only represent an

interesting imagery related to human sleep, but

could also be a basis for a conceptual framework for

artists and scientists to work with.

The paper is organized as follows. Section 2

discusses generative art and swarm art. Section 3

describes the KANTS algorithm used for generating

the EEG sleep images. In Section 4 the signals and

the sleep staging problem is introduced. Section 5

shows the images generated by the algorithm with a

set of sleep data recorded from sane adults. Finally,

Section 6 concludes the paper and outlines future

lines of work.

2 SWARM ART

Generative art is a term used to classify artistic

creations that, with more or less human intervention,

are mainly generated by artificial intelligence

systems or other computational models. There is an

enormous amount of work in the area, and

generative art is even gradually dividing itself into

subfields, such as artificial music, and evolutionary

art. From the large number of work created in the

last decades, we will describe just a few, more

related to the pherogenic drawings, technically or

metaphorically.

Like KANTS, Leonel Moura’s swarm paintings

(Moura, 2001) are also based on Chialvo and

Millona’s swarm model. The author started by

experimenting on-screen computer drawings, using

the ant system described in (Chialvo and Millonas,

1995). However, the results were disappointing until

he used a CAD machine and a brush to create

physical objects. Since then, Moura has been

experimenting with swarms, self-organization and

robotics (Moura, 2009).

Like Moura, Monmarché et al. (2007) also use

ants for their research on the potentialities of swarms

as “non-human artists”. The authors discuss the ant

paradigm as a tool for generating music and

painting.

Using a common terminology in the History of

Art, Moura and Monmarché’s swarm paintings may

be categorized as abstract, while the proposal by

Collomosse (2007), for instance, which uses

Evolutionary Computation to evolve aesthetically

appealing techniques for photo rendering, is more

related to figurative art. Semet et al. (2004) also

investigated the automatic generation of rendering.

The authors propose a method for non-photorealistic

rendering based on artificial ants. The ants move and

sense the environment (image) and deposit “ink” on

an output image, according to their location and the

state of a short term memory. The user interacts with

the ant colony, by choosing the parameters, defining

“importance maps” and deciding when the rendering

is finished.

In 2001, Ramos and Almeida (2001) proposed a

modification of the Chialvo and Millonas ant

systems in which the ants evolve on a grayscale

image (i.e., the 2-dimensional lattice stores the

pixels’ values of the picture) and detect the edges of

that image, generating pheromone maps that are

sketches of the environmental grayscale images.

Later, Fernandes et al. (2005) described an

evolutionary extension to the model that radically

changes the aspect of the pheromone maps. In 2010,

Fernandes (2010) proposed the term pherographia

(meaning drawing with pheromones) as a

designation for the resulting pheromone maps of the

system, and projected a line of creative work based

on pherographia that resulted in several artworks.

These artworks have been exhibited to an

heterogeneous audience — see (Moura, 2009) and

PherogenicDrawings-GeneratingColored2-dimensionalAbstractRepresentationsofSleepEEGwiththeKANTS

Algorithm

(Courchesne et al., 2009). In a sense, the pherogenic

drawings described in this paper are also

pherographs, since KANTS comes from the same

base-system, and the images are actually the

pheromone maps of the algorithm. However, we use

here the term pherogenic drawings in order to

differentiate from the images in (Ramos &Almeida,

2001) and (Fernandes et al., 2005), which are closely

related to photographia, the inspiration of the term

pherographia.

In fact, pherographia, as used by Fernandes,

results in typical figurative artworks, while the

swarm paintings presented in this paper are purely

abstract. The pherographs are created using a

photograph as a base-image; KANTS uses correlatd

data, which interacts in a heterogeneous

environment, “shaping” that same environment. Of

course, pherographia, since it imitates the base-

image, may also be used for creating non-figurative

works, as long as such kind of image is chosen as a

base-image. That is, pherographia relies much more

on the human decision, while the results given by

KANTS, as shown in Section 5, are more

unpredictable, since they depend on large quantities

of data, gathered from natural phenomena.

Pherographia and the above referred works do

not rely on an explicit objective function to guide the

exploration of the environment, but other approaches

require a fitness functions that must be optimized.

These approaches, usually termed as evolutionary

art, may be divided in two classes: automated and

interactive evolutionary art. Interactive evolutionary

art is based on interactive Evolutionary Algorithms

(EA) (Takagi, 2001). Interactive EAs use human

evaluation for determining the quality of the

solutions described by the population: i.e., one or

more humans evaluate the solution and provide the

algorithm with some measure of quality of the

individual or guide the search by interacting with the

reproduction process (human-guided EAs).

Interactive evolutionary art is based on

interactive and human-guided EAs. Karl Sims

(1991), for instance, used a human-guided EA for

generating 2-dimensional abstract forms. Sims has

an extensive body-of-work on artificial and

evolutionary art that has been exhibited in art

galleries and art festivals. Another important author

in this field is William Latham. Like Sims, he used

evolutionary algorithms and computer graphics in

the early 1990s to generate digital images (Todd and

Latham, 1992). Since then, several researchers and

artists have been working on interactive

evolutionary art, which has also been used in

combination with swarm art.

Aupetit et al. (2003), for instance, use an

interactive EA for evolving the parameters of a

swarm of artificial ants that interacts with the

environment (canvas). Each ant competes with the

other ants for color placement. Given a set of

parameters, the ants are able to draw complex

images, and they can even paint for several hours,

giving a different painting in each moment. The

sensory mechanism of the ants in (Aupetit et al.,

2003) was modeled in such a way that they are

responsive only to the luminance values of the

colors.

Greenfield (2005) follows a different approach

and uses ants that are responsive to tristimulus color

values. Furthermore, he uses a non-interactive EA

by designing fitness functions for evolving ant

behavior. Later, the author increased the complexity

of his model and designed ants that are responsive to

both environmental stimulus and other ants’ direct

stimulus, thus increasing the role of stigmergy in the

model (Greenfield, 2006).

These are just a few examples of swarm and

evolutionary art, more related to the work described

in this paper. There are many variants of generative

art and other authors have been providing interesting

compilations and state-of-the art reviews. Romero

and Machado (2007), for instance, edited a book on

evolutionary and artificial art that gathers some of

the most relevant proposals in the field. Lewis

(2007) gives an exhaustive review on the state of the

art, not only on interactive and human-guided

evolutionary art, but also on other types of artificial

art. In this paper, we aim at contributing to a

motivating field that blends art and science by using

the KANTS clustering algorithm as a swarm-art

creative tool. For that purpose, we use a simplified

version of the algorithm that is described in the

following section.

3 KANTS

The KANTS algorithm is an ant-based method for

data clustering and classification. The term KANTS

derives from Kohonen Ants, since the algorithm was

partially inspired by Kohonen’s Self-Organizing

Maps (Kohonen, 2001). However, KANTS is also

based on AS and its working mechanisms are very

similar to the algorithms in (Chialvo and Millonas,

1995) and (Ramos and Almeida, 2001). The way the

concept of pheromone is implemented is the main

difference when comparing KANTS with AS.

In this section, a simplified version of KANTS is

described. Since performance is not an issue here,

IJCCI2012-InternationalJointConferenceonComputationalIntelligence

the algorithm has been deprived of some parameters

that can be useful for fine-tuning its behaviour, but

are not fundamental for swarm art. The reader is

referred to (Mora et al., 2008) for a detailed

description of the original KANTS. Please note that

although KANTS is different from traditional Ant

Algorithms, it is stigmergic, and directly inspired by

AS: its working mechanisms are simple extensions

of the model’s set of equations. Therefore we use

here the metaphor and the terminology associated

with this kind of algorithms and models: ants,

pheromone, reinforcement and evaporation.

KANTS is based on the emergent properties of a

set of simple units that travel through a 2-

dimensional grid. In KANTS, this habitat is mapped

to an array with size , in which  is the

dimension of the data vectors of the target-problem,

and  is the dimension of the grid. That is, each

cell in the habitat is mapped to a -dimensional

vector. In addition, the ants also “carry” a -

dimensional vector that corresponds to a data

sample: each ant is in fact one data sample of the

data set. The main idea of the algorithm is having

data samples (ants) moving on (and updating a) an

array of real-valued vectors with the same size of the

samples. The dimension of the habitat affects the

performance. In general, a ratio between the number

of data samples and the size of the habitat (measured

in number of cells) in the range 



 provides

a good basis for KANTS clustering abbility.

The values of the grid’s vectors are initially set

to a random value with uniform distribution in the

range 0,1.0. Then, the ants are randomly placed in

the grid (after the vectors they “carry” are also

normalized within the range 0,1.0). In each

iteration, each ant is allowed to move to a different

cell of the habitat and modify that cell’s vector

values. The ants move to neighboring cells using

equations 1 and 2, taken from AS.









1



1





(1)



→









.rj

∑







∈ .

(2)

Equation 1 measures the relative probability of

moving to a cell  with pheromone density . The

parameter  (0 is associated with the

osmotropotaxic sensitivity. Osmotropotaxis has been

recognized by Wilson (1971) as one of two

fundamental types of an ant’s sensing and

processing of pheromone, and it is related to

instantaneous pheromone gradient following. In

other words, parameter  controls the degree of

randomness with which the ants follow the gradient

of pheromone. The parameter  (0defines the

sensory capacity (1

⁄

), which describes the fact that

each ant’s ability to sense pheromone decreases

somewhat at high concentrations. This means that an

ant will eventually tend to move away from a trail

when the pheromone reaches a high concentration,

leading to a peaked function for the average time an

ant will stay on a trail, as the concentration of

pheromone is varied.

Equation 2, which models the probability of an

ant moving to a specific cell in the habitat 

belonging to the current cell’s Moore neighborhood,

is defined after a discretization of time and space:



→

is the probability of moving from cell  to ,

 is given by equation 1 and  is set to 1 if the

cell  is within a user-defined radius centered on the

cell  (or any other type of permitted target-region

defined by the user) and 0 otherwise. The

pheromone density  in equation 1 is defined as the

inverse of the Euclidean distance 







,





between

the vector carried by ant  



and the vector in cell

, at time-step t, 



:









,







(3)

This way, an ant tends to travel to cells that are

mapped to vectors which are “closer” to its own

vector. (Please note that 



is a data sample and

therefore constant, while the vectors mapped by the

grid are modified by the ants). The ants update the

cell’s vector where they are currently on, according

to equation 4, where  ∈ 0,1.0 is a learning rate

that controls how fast the cells’ vectors acquire the

information carried by the ants. This is the equation

that modifies the environment and shapes the images

given in Section 5. Please note that this

reinforcement action is proportional to the Euclidean

distance between the ant’s vector and the cell’s

vector: an ant tends to travel to cells with vectors

more “similar” to its own, and, at the same time,

they change that cell’s values, approximating them

to their own values, at a rate that is proportional to

the distance between the vectors.

























1



1







,













.

















1



(4)





























.























(5)

Finally, the grid vectors are all evaporated in each

time step. Evaporation, in KANTS, is done by

updating the values according to Equation 5, where

∈0,1.0 (usually a small value, in the range

0.001,0.1) is the evaporation rate and 







is the

PherogenicDrawings-GeneratingColored2-dimensionalAbstractRepresentationsofSleepEEGwiththeKANTS

Algorithm

vector’s initial state (at 0). Basically, the

evaporation step pushes the vectors’ values towards

their initial values.

With this set of equations, the ants shape the

environment, communicate via that environment,

self-organize, and, after a certain number of

iterations, congregate in clusters that more or less

represent each class in the data set. Figure 1

exemplifies the outcome of KANTS’ stigmergic

behavior when applied to the iris flower data set

(Fischer, 1936). The iris dataset consists of 150

samples of vectors, 50 of each of three classes of iris

flowers. Each vector has 4 variables, representing

the 4 features from each sample. Therefore, KANTS

works with a population of 150 ants in a 20  20

habitat. Parameters  and  are set to 32 and 0.2

respectively, while  is set to 0.5 and evaporation

rate  is set to 0.01. Figure 1 shows the state of the

swarm at different time-steps. Each color represents

a class. After 50 iterations the ants start to cluster. At

  100, the Setosa cluster (red) is defined and

separated. Versicolor and Viriginica are not

separable but the algorithm has an interesting

capacity of congregating Virginica samples (blue) in

a region of the habitat. The stochastic nature of the

algorithm and the lack of any local refinement

mechanism makes that sometimes the clusters tend

to break (see   150). However, these results and

others (Mora et al., 2008) validate the algorithm as a

non-supervised clustering algorithm.

0 50

  100   150

Figure 1: KANTS: Evolution of the position of the ants in

the grid. Iris flower data set. Red samples: Setosa; green

samples: Versicolor; blue samples: Virginica.

Mora et al. (2008) also describe a classification

tool that uses information retrieved by the state of

swarm. However, the pheromone maps (i.e., the

grid) are used by the algorithm only for the ants to

communicate, being discarded by the end of the run.

The important components of KANTS as a problem

solver are the clusters and the classification maps.

Section 5 shows how the grid can be visualized as a

kind of data’s fingerprint. But first, Section 4

introduces the sleep staging problem and the data

used for generating the pherogenic drawings.

4 SLEEP SIGNALS

Sleep is a state of reduced and filtered sensory and

motor activity, within which there are different

stages, each one with a distinct set of associated

physiological and neurological features. The correct

identification of these stages is very important for

the diagnosis and treatment of sleep disorders.

However, sleep classification is not completely

standardized. Usually, sleep experts make the

classification by visual methods, i.e., they analyze

the signal and then, according to its patterns in a

specific time period, they decide in which stage the

patient was in that precise period. This method is

time-consuming and prone to errors. Therefore, it is

very important for biomedical sleep research to

devise methods to extract the proper information that

is later used for classification. Then, portable

devices may be used for monitoring sleep (Krejcar et

al., 2011) or for detecting sleep disorders (Acharya

et al., 2010). However, automatic sleep classification

is a hard computational problem that requires

efficient solutions at different levels of the process.

After extracting the relevant information from

the signals associated with sleep —

electroencephalography (EEG), electromyography

(EMG) and electrooculography (EOG) — competent

classification tools are also required for a correct

identification of the sleep stages. Even though

several attempts have been made to automate the

classification, so far no method has been published

that has proven its validity in a study including a

sufficiently large number of controls and patients of

all adult age ranges.

Usually, the classification of sleep stages is made

under the Rechtschaffen and Kales (1968) guidelines

(R&K classification rules), which divide sleep into

five stages: REM, NREM1, NREM2, NREM3 and

NREM 4, with WAKE as an additional stage. The

complete EEG, EOG and EMG records, divided in

epochs, usually, each one with 30 second.

Therefore, an 8-hour night-sleep consists in 960

samples of six possible classes.

IJCCI2012-InternationalJointConferenceonComputationalIntelligence

An automatic tool for classifying sleep data can

be constructed under two different principles. In the

first approach, the manual classification is mimicked

and translated into an automatic process. Another

approach extracts relevant information from the

signals, quantifies it and then use traditional

numerical classification system. In 1975, Hjorth

(1975) proposed a method for extracting three

parameters from EEG. The first is a measure of the

mean power representing the activity of the signal.

The second, called mobility, is an estimate of the

mean frequency. The third estimates the bandwidth

of the signal and represents complexity. The main

advantage of Hjorth’s method is its low

computational cost when compared to other

methods. Furthermore, the time-domain orientation

of this representation may prove suitable for

situations where ongoing EEG analysis is required.

Figure 2: Hypnograms of patients 1, 2, 3, 4 and 5

(top to bottom). States, y-axis: 1 (NREM1); 2 (NREM2); 3

(NREM3); 4 (NREM4); 5 (Awake); 6 (REM).

However, our choice of the Hjorth parameters is

merely practical: the three variables may be directly

translated into RGB values, generating the desired 2-

dimensional representation of sleep. Besides Hjorth

parameters, there other feature extraction methods.

In fact, this is still an open problem. This paper does

not deal directly with the sleep staging classification

problem and therefore, novel techniques for

extracting relevant features from the sleep signals

are not required. The following section describes the

resulting KANTS pheromone maps when applying

the algorithm to a set of Hjorth parameters

describing EEG signals of five adult sane patients.

5 EXPERIMENTS

For testing KANTS and retrieving its pheromone

maps as RGB images, real data from five adult sane

patients were used. The patients are labeled 01,

02, 03, 04 and 05. The EEG signals were

analyzed and each epoch classified within one of the

R&K classes by a medical expert team. Then, the

Hjorth parameters were extracted from those EEG

signals. Five files with the parameters corresponding

to the EEG signals of each patient were created. The

files contain 844,907, 769, 685 and 865 samples,

respectively, from 01 to 05. Each vector is

labeled with the class assigned by the experts. Since

there are three parameters in the data set, the ants are

described by 







,



,



, where 



is the

Hjorth activity value in the data set, 



is the

complexity of the same vector in the data set value

and 



is mobility value (see equation 3).

Figure 2 shows the hypnograms of some patients.

A hypnogram is a graphical representation of the

stages of person’s sleep in a time-domain that allows

a quick observation of a night’s sleep and the

identification of possible sleep disorders. This study

uses data from sane adults without diagnosed sleep

disorders, which, if present, would disturb a normal

hypnogram, but it is possible to observe that each

patient generates rather different hypnograms. When

applied to a stochastic algorithm like KANTS, it is

expected that the resulting pheromone maps are also

very different.

KANTS habitat size is set to 200  200. With this

size, the ratio between the number of ants and the

number of environmental vectors is much smaller

than the values suggested in (Mora et al., 2008).

However, the objective of this work is not to

optimize the clustering ability of KANTS, but

instead to generate images during the process. Given

the size of the data sets, the suggested ratio would

generate small images that could not be properly

visualized and valued. Therefore, input files of each

0 100 200 300 400

time(minutes)

PherogenicDrawings-GeneratingColored2-dimensionalAbstractRepresentationsofSleepEEGwiththeKANTS

Algorithm

patient’s data with 10 copies of each sample were

created. The results in this section are the

pheromone maps created by these enlarged sets,

with sizes 8440 (01), 9070 (02), 7690 (03),

6850 (04) and 8650 (05).

Figure 3: Pherogenic drawing of 05 sleeping period.

Figure 4: Pherographic drawing of patients 01 (top-left),

02 (top-right), 03 (bottom-left) and 04 (bottom-right).

Figure 5: Pherogenic drawing mixing the pheromone maps

generated by 01, 02 and 03.

The algorithm was tested with the following

settings. Parameters  and  are set to 32 and 0.2.

These values are in the range of the parameter space

that in

(Mora et al., 2008) puts the system in the self-

organized state.

Learning rate  is set to 0.2 and

evaporation rate  is set to 0.0025. The algorithm

stops after 50 iterations and the environmental

lattice at 50 is used to generate the images in the

RGB format. Each set of values was stored in

200  200 arrays, each one being the source for

creating an RGB image: activity related values are

used to model R values, while G and B are defined

by complexity and mobility, respectively. The

resulting image of patient 05 is shown in Figure 3

while Figure 4 shows the drawings of patients 01to

04. It is clear that each night’s data set generates

unique drawings, even if there are common features

to all of them. However, each one shows different

patterns and major differences are also observed,

namely in the dominant color of the drawings: 01,

for instance, has a strong presence of a pinkish color,

that is almost absent from the other pictures (except

04, where light patches of rose are present).

If we abandon the project of a univocal

representation of a night’s sleep, the possibilities are

endless. It is possible, for instance, to combine the

maps generated by different data sets. Figure 5

shows the result of mixing the environmental

vectors. The image uses for R the activity-related

vectors generated by 01 data, G values are set by

the complexity values generated by 02, and B is

defined by the mobility values of the environment

shaped by patient 03. With such an uncorrelated

input, the picture is more dynamic and vivid than the

images generated by a single night’s sleep.

Figure 6: Distribution of the samples over the class-

domain (the classes are assigned by the medical experts).

100

200

300

400

500

123456

numberofsamples

classes

p01

100

200

300

400

500

123456

classes

p02

100

200

300

400

500

123456

numberofsamples

classes

p03

100

200

300

400

500

123456

classes

p04

IJCCI2012-InternationalJointConferenceonComputationalIntelligence

Although the hypnograms are clearly different

for each patient, such state-time representations of

the sleep do not help to interpret the differences

observed in the pherogenic drawings of each patient.

The main characteristics of the hypnograms are

perceived in the time-domain. However, for

KANTS, the sequence of events is not relevant. The

behaviour of the algorithm only depends on the

values of the samples, not on their order. Therefore,

for interpreting the differences between the

drawings, it is better to analyze the distribution of

samples in each patient, as in Figure 6.

By comparing the distribution of 01 with other

patients, the main difference is its reduced number

of class 4 (NREM4) samples. This fact could

explain why the pherographic drawing of 01 has a

clear distinct palette of dominant colors. As for03,

which generates a picture with darker tones, its ratio

between class 6 and other classes is clearly higher

than in other patients. This could explain its unique

tone in the set of pherogenic drawings. These

hypotheses are hard to demonstrate due to the

stochastic nature of KANTS and the high number of

variables involved in the process. However, it is

expected that radically different distributions

produce different images, since the samples are the

artists here: they act upon the environment, shaping

it, and the result of such actions depend on the

values of the samples. Therefore, different samples

may create different patterns.

Being a art project, there is an unavoidable (and

desired) subjectivity in this work. However, for the

authors, the results are motivating, not only

creatively, but also as a science-art experience. For

long, sleep was a mysterious state that science and

philosophy tried to study and interpret. In addition,

dreams, an inseparable feature of human sleep,

added a mystic aura to this physiological state.

Having the opportunity of generating representations

of sleep with a bio-inspired and self-organized

algorithm is surely inspiring. Furthermore, the whole

process is based on a kind of distributed creativity,

i.e., the drawings are in part generated by the patient,

since the data samples shape the environment, and in

part created by the swarm and its local rules, from

which global and complex behaviour emerges.

6 CONCLUSIONS

This paper describes a swarm art experiment

conducted with an ant-based clustering algorithm

called KANTS. The algorithm is able to create

clusters of data samples by letting those samples

(ants) travel trough a heterogeneous environment.

The ants communicate via the environment and

modify it. This work uses the resulting environment

(pheromone maps) to create 2-dimensional color

representation of data sets. In this case, sleep data is

used. The input of the algorithm is the well known

Hjorth parameter set, which describe the EEG signal

in the time-domain. The resulting images are

aesthetically interesting, with dynamic patterns and

colors that spread through the canvas in a balanced

way. They also have the interesting characteristic of

being unique representations of a night’s sleep. The

pherogenic drawings of human sleep are fingerprints

of a person’s night sleep. Furthermore, they are the

result of a distributed creativity, in part generated by

the person/patient (or by the data generated by the

patient during the sleep period), and in part created

by the swarm and its local rules, from which global

and complex behavior emerges.

There are still some technical issues that limit the

size of the environment, and therefore the size of the

images. The computational time of the KANTS

algorithm grows at least linearly with the number of

vectors in the habitat, which means that a 2000 

2000 size image requires a computational cost that

is 100 times the cost of creating a 200 200 sized

image. Since creating 200  200 pheromone maps

takes 10-15 minutes, experiments with much larger

sizes may be impractical at the moment.

Sleep data with Hjorth parameters was chosen

because the three parameters are suited for a direct

translation into the RGB format. However, other

feature extraction methods of the EEG signal could

be used, providing that strategies for translating the

values into the RGB image are devised. In addition,

other type of data can also be tested. There are many

benchmark problems and real-world data sets and it

would be interesting to observe the resulting

pherogenic drawings after different types of data.

Another possibility is to create 3-dimensional

objects, in which a fourth parameter shapes the

object in a third axis.

ACKNOWLEDGEMENTS

The first author wishes to thank FCT, Ministério da

Ciência e Tecnologia, his Research Fellowship

SFRH / BPD / 66876 / 2009, also supported by FCT

(ISR/IST plurianual funding) through the

POS_Conhecimento Program. This work is

supported by project TIN2011-28627-C04-02

awarded by the Spanish Ministry of Science and

PherogenicDrawings-GeneratingColored2-dimensionalAbstractRepresentationsofSleepEEGwiththeKANTS

Algorithm

Innovation and P08-TIC-03903 awarded by the

Andalusian Regional Government.

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