Beside the drawing that we have observed previously, some of batik patterns actually has shown a repetitive process in the making and can be easily recognized. For example is the well known motif parang. This is a very famous batik motif and there have also been a lot of batik patterns made by the innovation of the motif that is drawn in diagonal form runs parallel to each other repetitively. This motif have some disputed representation, for the word parang can be related to a “sword” (Malayan language) while there are also the old Javanese word referring it to “slope of canyon”. The parang origins in unknown times and original designers, but some people traced it back to the times of Raden Panji, the hero from the 11th century East Javanese Kingdom of Kediri and Jenggala [13]. Interestingly, the diagonal form of the motif can be observed as a set of the iterated function system’s attractors as depicted in figure 3. Interestingly the Chaos Game applied to the attractor would emerging patterns that could lead to the repetitive style of the motif.

Understanding the iterated mechanisms on making the basic motif of batik reveals the elementary cognitive process on making the batik designs. As we have the model of the design-making of batik mathematically, then we have practically a great deal of motif stocks in our computational warehouse. An algorithm of “chaos game” as introduced in [1] can be incorporated computationally by applying the affine transformation with its respective probability. Chaos game is conducted by using randomly picked a point in the drawing-space as initial condition and then with certain probability (the seventh columns in our table 1 and 2). The resulting point is then dotted and becomes the input for the next iteration and so on. The dots would eventually emerges the pattern of which our affine transformations attract them. While we remember the etymological meaning of batik as “drawing dots”, this becomes more interesting for the patterns we have from the Chaos Game are also emerged from the “attracted” dots.

Moreover, as we have understood the deconstruction of the basic motif of batik in the fashion of affine transformation, then we can apply a great deal of other simple and beautiful result of iterated function system as a source for exploration in the innovation of batik pattern as well as creating new basic one. From the acquisition of the iterated function systems and the Chaos Game fractal models, we can therefore in the space of quest for creativity with computationally generated batik motif, at least by implementing these two applications:

– Slight Modifications on the variables of the known batik affine transformations The sawat motif, for example, is now able to be produced in its various forms and pattern for changing the numbers in the matrix as showed in table 1. We can imagine how many possible basic motif for batik designs that we can explore computationally, be it for the batik production or even for any other motif related creative fields. Related to the chaos and fractal theory, sometimes a simple and small changes on the coefficients could bring a lot of changes in the emerging pattern. Some of the patterns yielded in our arbitrary experiments on the sawat generative are presented in figure 4. While batik is a traditional patterns with self-similarity aspects, this opens and even broader field for computational generated motif that can enrich batik models.

– The incorporation of simple models of iterated function system in order to mimick things that can be applied as source for batik designs. As it has been discussed in [1] as well as the discourse related to aesthetics and mathematics in [5] as well as [9], with more specific compositional designs of batik [10], when fractal mathematics can explain some generative process of beautiful patterns known in the domain of art, they can also be employed to inspire the new methods on generating art. Our Iterated Function Systems mimicking batik and the computational process of the Chaos Game thus can be used to inspire and broadened the study of batik as generative art. Some of the examples made from transformed triangles in elementary form is shown in figure 5. It is interesting to notice how the triangles can be eventually transformed into slightly different patterns.

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