The paper discusses some aspects of Iterated Function System while referring to some interesting point of view into Indonesian traditional batik. The deconstruction is delivered in our recognition of the Collage Theorem to find the affine transform of the iterated function system that attracts the iteration of drawing the dots into the complex motif of – or at least, having high similarity to – batik patterns. We employ and revisit the well-known Chaos Game to reconstruct after having some basic motifs is deconstructed. The reconstruction of the complex pattern opens a quest of creativity broadening the computationally generated batik exploiting its self-similarity properties. A challenge to meet the modern computational generative art with the traditional batik designs is expected to yield synergistically interesting results aesthetically. The paper concludes with two arrows of our further endeavors in this field, be it enriching our understanding of how human cognition has created such beautiful patterns and designs traditionally since ancient civilizations in our anthropological perspective while in the other hand providing us tool to the empowerment of batik as generative aesthetics by employment of computation.

Traditional Indonesian Batik shows interesting fractal geometry and it has also been demonstrated practically that this property could broaden the acquisition of batik as model to generative art rooted from the traditional heritage [10]. While we have recognized the steps of making the batik crafts [3], the computations of the innovative landscape of batik designs are now providing borderless creations of design applicable to enrichment the available traditional motif1. However, we can leave batik compositional design as an artificial generative art while we can delve deeper into the batik basic motif designs by deconstructing them.

We use the term “deconstruction” here by borrowing it from the terminology often used in philosophical or (post)-modern literary texts, roughly meant as finding meanings that were not originally intended by an author, composer, or artist of a cultural object (cf. [6]). Thus, here we use the terminology of batik deconstruction to denote a process decomposing a traditional motif in a way possibly different from the one used in the making and fabrication of the batik in general. As the purpose of the “deconstruction” in literary and philosophical is (perhaps) to understand the intangible things in the production of cultural object; here we incorporate the iterated function system and some conceptual related to it to understand the interesting self-similarity in the micro- sense of batik designs: the basic motif – a feature that is possibly an indirect intention when it is designed at the first place. While there have been some efforts to “deconstruct” traditional designs mathematically in some other places of ancient civilizations around the globe, batik is still left untouched without deep realizations in its mathematical aspects.

The batik process, represented by the word “mbatik” etymologically is realized most likely come from the Javanese phrase: “amba titik”, meaning “drawing little dots”. Here, the suffix “tik” could mean “little dot”, “drop”, or “point”, however, it can also denote a ticking or trapping sound. In relation of batik designs with its function as fashion ornamentation, the root meaning of the suffix might also be seen in Javanese words such as “tritik” (a resist process by which designs are reserved on textiles by sewing and gathering before the dyeing process), or “nitik” (a design of batik imitating the weaving patterns). In short, we can always refer that mbatik is a representation of the drawing, painting, or writing [4]. Any drawings however, although not necessarily, would always be able to be understood elementarily as dotting. This is directly related to our further discussions on the iterated function system in the rest of the paper.

Iterative processes can be defined as repetitive steps that applied into the output of a system back as an initial state. Here, the output becomes the input and so on while the applied steps in the process do not have to same to all kinds of input but yet similar. The Iterated Function System regards the process with particular transformations that are applied repetitively with some geometric constraints yielding the self-similar patterns that we recognize as fractals. Thus, iterated function system is a way to have fractal geometry. The famous Multiple Reduction Copying Machine (MRCM) is an example to understand the iterated function system. MRCM regularly copies an image with some arrangements such that reducing the size of the origin while overlapping copies of the origin into the generated copy.

The Iterated Function System is a system as a feedback loop in which the output of the previous copying process is used again as input of the next round of copying process. Interestingly, it does not matter with what picture or what points the input initially begin with, the resulting will eventually be “attracted” to certain fractal pattern. Thus, the problem of the deconstruction batik through the iterated function system is to reveal the attractors that made a fractal image as what it is.

The paper discusses basic motif of batik designs as the iterative drawing of dots emerging the well- known pattern as we perceive. Here we already have a first step in deconstructing batik designs. We begin with discussion on model we use to generate fractal images, the Iterated Function System, the Barnsley’s collage theorem [1], and some geometrical transformations incorporated composing fractal images. This is followed by the discussions on batik basic designs and the more likely affine transformation producing the designs. Eventually, we outline some conjectures and open problems to understand batik as a very interesting cognitive representation on aesthetics among Indonesian people, especially those with Javanese tradition. This however, broadens our endeavors to generally deconstructing batik.

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