Application of the Fractal Geometry in Development Surya Majapahit Batik Motif

Abstract

The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and zooming to explore different regions of the sets. TThe Mojokerto Surya Majapahit batik motif is a motif that has eight corners. One way to develop a Mojokerto batik motif that is similar to Surya Majapahit is by applying the science of fractal geometry. Fractal geometry studies a fractal pattern that can change shape according to input parameters and the number of iterations carried out. This research was conducted to determine the application of Mandelbrot and Julia’s fractal geometry using geometric transformations to obtain batik motif variants that is similar to Surya Majapahit. There are three steps in forming this motif variant. First, generating Mandelbrot fractals and Julia fractals. Second, the patterns generated by Mandelbrot and Julia are applied using geometric transformations. The geometric transformations that will be used are rotation, dilation, and translation. Finally, these patterns will be modified by combining patterns implementing logic operations using Python computer applications. The results of this research obtained four variants of batik motif that is similar to Surya Majapahit. The difference in each variant lies in the order of transformation. Variant 1 and variant 3 can be carried out by changing the sequence of geometric transformations, namely rotation, translation and dilationVariant 1 is obtained by applying rotation, dilation, and translation to the Mandelbrot and Julia pattern. Variant 2 is obtained with the Mandelbrot pattern applying rotation, dilation with two different scales, and translation, while the Julia pattern only applied rotation and translation. Variant 3 is obtained by applying rotation, dilation and translation to the Mandelbrot and Julia pattern. Variant 4 is obtained with the Mandelbrot pattern applied by rotation, dilation with three different scales, and translation, while the Julia pattern was applied only by rotation and translation. Meanwhile variants 2 and 4 apply different rotations, dilation scales, namely 0.451 and 0.318, and translation to the Mandelbrot pattern.