Batik Fractal : Traditional Art to Modern Complexity
Muhamad Lukman, ST, MT
Pixel People Research and Design Group,
Bandung Institute of Technology, Bandung, Indonesia
Dept Dynamical System, Bandung Fe Institute,
email : email@example.com
Drs. Achmad Haldani Destiarmand, M.Sn
Faculty of Art and Design,
Bandung Institute of Technology, Bandung, Indonesia
Fractal Dimension Analysis with Fourier Transformation for Batik shows the presence of
fractal with range between 1 and 2. The Isen process ( filling smaller motifs after the
bigger motifs are done ) is a significant factor which made the Self Affine,a fractal’s
characteristic, appear. Analysis of Variance/ ANOVA Test for Fractal Dimension
classified several batiks that have similar value, according to their motifs and their place
of origins. Furthermore, Fractal Dimension spreads almost symmetrically in every angle,
except for banji motifs where the symmetry appears less. According to their place of
origin, Yogya and Solo has similar Fractal Dimension with batik from Madura and Garut,
but Madura and Garut themselves has different Fractal Dimensions.
The presence of fractal in batik indicates the presence of complexity in this traditional
art. The complexity emerges because the effort to obey pakem rule (symbolic
meanings, harmony, symmetry) and media limitations (canting, wax)
Keywords: batik, isen, fractal, Fractal Dimension, Self Affine, Fourier Transformation
Batik and Fractal Dimension: An Introduction
Batik is considered to be a textile art. The character of this particular art extents from
ethnography, archaeology, anthropology, tribal art, primitive art, and traditional visual art. Basic
technique in producing batik has been widely known, such as India (bandhana), China (miao),
Japan (rokechi,katanori), Russia (bokhara), and Malay region (plangi, palekat).
Batik motifs itself evolves according to their place and time, such as keraton (solo, yogya,
majapahit), India (patola and jlamprang), Islam (anti-anthromorphic, arabesque, flat forms),
China (bright colour, floral, phoenix, lions and dragons) and even dutch influenced Indonesia.
Because batik has certain symbolic meaning, then each object which become batik
ornamentations has mythological meanings. Animal motifs use many bird objects due to its flight
capability that can connect between heaven and earth. So does lotus motif, a water plant, as a
manifestation of life since it grow upward to the sky from the depth of water.
There are two main topics in defining batik: as a process and as motif. Process is the technic in
craftsmanship to produce batik by resist-dye technique. The motifs itself is the ornaments found
in batik, which are classified as parang, geometry,banji, spreading plants, water plants, flowers
Batik is not an ordinary textile art. Inside we found functional value. This value creates different
batik motifs. For example the motifs between peasant and noble, coastal and interior, everyday
and ritual are not similar to represent the difference of each value.
In aesthetic side, the quality is not based on the judgment of being good or bad, but in its effort to
obey the pakem rule. As a form of decorative art, the ornament or isen is not merely to fill the
space left from the batik motifs, but rather as to give specific value. Indeed, to understand the
batik motif it is not enough to disentangle the motifs to just merely dots, line, colour or shape,
but also its meaning behind it.
In Complexity Theory, the emergent of Chaos are marked by the presence of fractal. Fractal
stands between order and chaos, in which case are known as in Edge of Chaos. Fractal can be
seen by its characteristic, which is Self-Similarity and Self-Affine. In Self-Similarity an object
has geometrical form which resembles the object’s detail in smaller scale. In Self Affine an
object has detail which resembles the object, although not necessarily be similar in every aspect.
This paper examines the process of batik in producing batik motifs which has fractal
characteristic. The initial Hypothesis of this research is that batik has fractional fractal
dimension, which means that batik is Fractal. The hypothesis’ background is the making of isen
in batik motifs. Isen itself is the process of filling the space left by main motifs with
The measurement of fractal dimension itself is useful for analyzing in different fields. Such as
heart failure detection ( Teich et al ), river flows (Szustalewicz et al), transportation (Dorfman),
brain tumor detection (Marsh), fish’s neuron in brain ( Isaeva ), retinal eye scan (Ewe et al).
The paper thus explores the possibility of creating batik through Generative Arts. If batik is
indeed fractal, then it is appropriate to produce batik motifs using the same means. The algorithm
is as follow:
Drawing batik using fractal
Adjusting variables to produce desired main motifs
Checking Fractal Dimension
Df doesn’t match
Figure 1, algorithm of creating batik using fractal as mean of Generative Art
The paper’s systematic consists of Preface, Methodology, Analysis, Conclusion and Suggestion
for Further Works.
Fractal dimension are defined by this expression:
Suppose Z is a picture with M X N size, with value for each pixel is f(x,y), then:
Indeed, the Fourier Transformation will be:
Value for each pixel is defined as G, whereas:
Value for each W are grouped in angle parameter ( with different m angle ) and distance (
different n length ), with
Figure 2, coordinate distribution
Figure 3, Df algorithm
Data in this analysis are from several region that produces batik in Java from Batik Komar
collection and Nian Djoemena. Picasso paintings (from 1989-1940) are included as comparative
object to test the validity of Fractal Dimension analysis. Each picture in this analysis has 200 X
200 pixel size, with m = 24 and n = 30.
To further illustrate Fractal Dimension in objects, below are several picture along with the
analysis of Fractal Dimension.
Fractal Dimension in each object that does not has fractal characteristic; empty space (df=0), line
contour (Df=1,099), plane contour (Df=2,011), and sphere (Df=3,040)
Based on Fractal Dimension Analysis trough Fourier Transformation, it is shown above each
dimension is not natural numbers whereas they supposed to an integer of 1 or 2. The explanation
is because the Analysis also calculates angle parameter and length from each point to centre
point of picture. But in general the rounding off to nearest natural number show that Fourier
Transformation is able to calculate the dimension from each picture. Object in picture 3 which
depicts three dimensional forms from mathematical equations can even be calculated as three
dimensional object although in two dimensional media. Then what would happen to object made
From Figure 4 it is shown that aspect of colour is important in analyzing Fractal Dimension. The
change from 0 dimension (empty space) to 1 dimension (line) needs curve to fill the empty
space. Furthermore the change from 1 dimension to 2 dimension ( plane ) needs colour to fill the
space. And the change from 2 dimension to 3 dimension need certain colour gradation for giving
the effect of 3 dimensional forms.
Fractal dimension of Picasso’s work according to time period. The Fractal dimension for each
period is near 3, which is conforms to the fact that Cubism depicts 3 dimensional object.
In Picasso’s work, there are slight differences in Fractal Dimension in each period. Although it is
still consistent with Cubism style which has ranges around 3, the 1921-2930 period has higher
dimension. It means that the detailing level in that period is particularly high. But in general all
of Picasso’s work does not show the presence of fractal. What about batik?
Figure 6a, motif
Batik is different than Picasso’s painting. It is clearly evident by comparing the Figure 4 with
Figure 5a. It is seen that batik motifs’ Fractal Dimension ranges between 1 and 2, even though
the object of the batik motifs is in 3. It shows that the pakem rule in making batik is to draw
objects which has dimension between 1 and 2, specifically in the range of 1.5 In other words
batik motifs appearance is between a curve and a plane.
The value of this particular dimension shows the presence of high detailing level in batik. This is
because the “isen” process in batik making. In this process, the empty space left by the main
motif are being filled by ornaments that fits the main motif. In batik, the isen is not just merely
filling the empty space but also a way for perfecting the entire motifs and giving batik its
meaning. From its symmetry by seeing the variance value (distribution of its average value), it
shows that banji motifs (batik index no. 62-65 in appendix) are the most asymmetrical compared
to other motifs, with highest variance level for Fractal Dimension of 0.0307. It can be seen by the
fluctuation of Fractal Dimension in angle 0, 90, 180, and 270, which is close to dimension 2
(plane). It raises interesting topic about the meaning of banji motifs itself, which closely related
to the tradition of weaving rattan to create planar forms.
Fractal dimension and the symmetry of each motifs
Besides banji motifs, according to Table 1 all motifs are symmetrical. In symbolic meaning the
symmetry itself symbolizes harmony and balance. Even though the object in batik motifs, such
as animals or plants are 3 dimensional forms, but the drawing style makes these object less than
2 dimensional and symmetrical. For example In Kupu Gandrung/ Butterfly in Love motifs (batik
index 167) which shows the effort to present the symmetry of butterfly by depicting the form in
spreaded wing. In Kawung motif (batik index 34-36). Or in Ceplokan flower motifs (batik index
121-126), the effort to create symmetry is being done by drawing batik motifs seen from above.
Interestingly, the most symmetrical condition are being shown by animal motifs, which has
lowest variance value in Fractal Dimension.ANOVA Test for Fractal Dimension in Figure 6b
and 6c shows four categories of different Fractal Dimension of batik motifs.The first category is
water plant and animal with Fractal Dimension of 1,4, second is spreading plant of 1,5, third is
parang, geometry and flower of 1,65, fourth is banji of 1.8.
ANOVA Test for each motifs, which shows their proximity to other motifs
Anova Test which shows 4 categories with different Fractal Dimensions.confidence interval 95%
Batik motifs produces different Fractal Dimensions. But the difference is still consistent with
batik motifs in general whereas batik is fractal with its dimension ranging from 1 to 2. The next
examination would divide batik into groups according to their place of regions they produce. In
everyday life, people often divide batik into their region it produces, such as Cirebon,
Yogyakarta, Solo, Tasik, etc. How would these effect batik’s Fractal Dimension?
Fractal Dimension of batik samples for each region with ANOVA Test shows that each regions
has different dimensions. Anova analysis categorizes batik according to its Fractal Dimension.
In first category with Fractal Dimension of 1.1 is only from Batik Cirebon as its member. In
second category of 1.3 – 1,4 are from Batik Solo, Garut, Yogyakarta and Madura. In third
category of 1.25 are from Madura, Yogya, Solo as its member. Fourth member of 1.4 are from
Madura, Yogya, Solo. Fifth member of 1.6 are from Lasem and Tasik.
In second, third and fourth it shows that Fractal Dimension of Batik Madura and Garut has
resemblance with Batik Yogya and Solo. However Batik Madura and Garut are different in their
dimension. This means that Batik Yogya and Solo influenced Madura and Garut. In relation with
its geographic place this analysis will prove interesting, since Solo and Yogya are situated in
Central Java, whereas Madura is in the east, and Garut is in west.
The ANOVA Test also shows that Batik Cirebon has singular Fractal Dimension, contrary with
other region. The result is in accordance with the fact that ornamentation of Batik Cirebon has
different perspective in principal and expression.
Fractal Dimension Analysis of batik, be it in motifs or regions, shows the presence of Fractal.
This resulted in interesting question: why does Batik has Fractal properties? To answer this, we
first must examine the characteristics of Fractal. Self-Similarity and Self Affine of an object
means that smaller scale in detail it exists geometry which resembles the object. The Isen
Process gives significant contribution in detailing in smaller scales. Because the isen does not
have to be necessarily the same with the motif, and Batik often has isen which resembles its
main motifs but not in scale or angles, then Self-Affine characters is most likely to be found in
Batik. Another interesting part in batik process is in the distribution of fractal properties in Batik,
which is uniform. This can be answered when we remember the concept of batik as a symbol of
harmony and balance. In closer observation, the process of creating batik involves the reduction
of dimension of objects that has three dimensional properties (animal, floral motifs). Not only
that, the resulted dimension has fractional properties. Besides the involvement of pakem rules, it
also related to media and tools of producing batik: textiles, canting to wax the textiles, and wax.
The limitations of media and symbolical meaning behind Batik makes its dimensions exists
between 1 and 2.
Fractal dimension of batik according to their regions.
Anova testing for classification of Fractal Dimension according to region, which resulted in five
category. Batik Cirebon has Fractal Dimension which is different than batik from other regions.
While Fractal Dimension between 1.2 and 1.5 has classification that is juxtaposed between Madura,
Yogya, Garut and Solo. Batik Lasem and Tasik is in Fractal Dimension of 1.5 – 1.7 classification.
Fractal Dimension Analysis through Fourier Transformation is able to calculate dimensions from
two dimensional pictures. The analysis for classification of batik according to motifs and regions
shows that Batik has fractal properties, which are evident in their dimension properties (1.5).
Batik stands between the curvature and plane. Furthermore the fractal properties shows high
degree of details. The details in different scales are the result of Isen process in Batik.
In terms of Generative Arts, Fractal Dimension can be used to control the batik that is produced
using fractal. Pixel People Group of Indonesia has develops computer software to produce
batiklike forms that uses Fractal Dimension to control the batik motifs. The batik is called Batik
Fractal. Using PHP language program, this software aims to design batik motifs in contemporary
or traditional means. The nature of PHP as free software also allows its user to develop this
program to future needs.
Aouidi, J., and Slimane, M.B. Multi-Fractal Formalism for Quasi-Self-Similar Functions. Journal
of Statistical Physics, Vol. 108, Nos. 3/4, August 2002 (© 2002).
Barron, U.G., and Butler, F. Fractal texture analysis of bread crumb digital images. Eur Food
Res Technol DOI 10.1007/s00217-007-0582-3
Culik, K. and Kari, J. Computational fractal geometry with WFA. Acta Informatica 34, 151–166
(1997) cSpringer-Verlag 1997
Currey, J.D., Kaffy, C., and Zioupos, P. Tissue heterogeneity, composite architecture and fractal
dimension effects in the fracture of ageing human bone. International Journal of Fracture (2006)
139:407-424. Springer 2006
Djoemena, Nian S. Ungkapan, Batik dan Mitra, Djambatan, 1986
Dorfman, J.R. Fractal Structures in the Phase Space of Simple Chaotic Systems with Transport.
P. Garbaczewski and R. Olkiewicz (Eds.): LNP 597, pp. 193–212, 2002.Springer-Verlag Berlin
Ewe, H.T. and Lee, P.S. Individual Recognition Based on Human Iris Using Fractal Dimension
Approach. D. Zhang and A.K. Jain (Eds.): ICBA 2004, LNCS 3072, pp. 467-474,
2004.©Springer-Verlag Berlin Heidelberg 2004
Georgsson, F.,Jansson, S., and Ols´en, C.Fractal Analysis of Mammograms. B.K. Ersbøll and
K.S. Pedersen (Eds.): SCIA 2007, LNCS 4522, pp. 92–101, 2007.Springer-Verlag Berlin
Heurteaux, Y. and Jaffard, S. MULTIFRACTAL ANALYSIS OF IMAGES: NEW CONNEXIONS
BETWEEN ANALYSIS AND GEOMETRY. J. Byrnes (ed.), Imaging for Detection and
Identification, 169–194. 2007 Springer.
Isaeva, V.V., Pushchina, E.V., and Karetin, Y.A. The Quasi-Fractal Structure of Fish Brain
Neurons. Russian Journal of Marine Biology, Vol. 30, No. 2, 2004, pp. 127–134. Original
Russian Text Copyright © 2004 by Biologiya Morya, Isaeva, Pushchina, Karetin.
Jelinek, H.F., Cornforth, D.J., Roberts, A.J., Landini,G., Bourke, P.,Iorio, A. Image Processing of
Finite Size Rat Retinal Ganglion Cells Using Multifractal and Local Connected Fractal Analysis.
G.I. Webb and Xinghuo Yu (Eds.): AI 2004, LNAI 3339, pp. 961–966, 2004. © Springer-Verlag
Berlin Heidelberg 2004
Kouzani, A.Z.Classification of face images using local iterated function systems. Machine Vision
and Applications. DOI 10.1007/s00138-007-0095-x.
Marsh, R., Jia, W., and Iftekharuddin, K.M. Fractal analysis of tumor in brain MR images.
Machine Vision and Applications (2003) 13:352-362. Machine Vision and Aplications, Springer-
Siu, W.C., Lam, K.M., Guo, B., and Lin, K.H. Automatic Human Face Recognition System Using
Fractal Dimension and Modified Hausdorff Distance.H.-Y. Shum, M. Liao, and S.-F. Chang
(Eds.): PCM 2001, LNCS 2195, pp.277–284, 2001.Springer-Verlag Berlin Heidelberg 2001
Strichartz, R.S. Pieeewise Linear Wavelets on S i e r p i n s k i Gasket Type F r a c t a ls. The
Journal of Fourier Analysis and Applications Volume 3, Number 4, 1997
Szustalewicz, A., and Vassilopoulos, A. Calculating the Fractal Dimension of River Basins,
Comparison of Several Methods. Biometrics, Computer Security Systems and Artificial
Teich, M.C. and Turcott, R.G. Fractal Character of the Electrocardiogram: Distinguishing Heart-
Failure and Normal Patients. Annal of Biomedical Engineering. Vol. 24, pp.269-293. 1996
Vasselle, B., and Giraudon, G. A multiscale regularity measure as a geometric criterion for
image segmentation. Machine Vision and Applications (1994) 7:229-236.Springer-Verlag 1994