Batik Jlamprang with Koch snowflake and Koch anti-snowflake fractal geometry using Desmos

Abstract

Batik Jlamprang is a cultural heritage from Pekalongan. This batik motif has a round shape and floral ornaments. The motif of batik Jlamprang is similar to the Koch snowflake. Mathematically, batik Jlamprang can be categorized as one of the shapes of fractal geometry. There are many known shapes of fractals, some of which are Koch snowflake and Koch anti-snowflake. The difference between Koch snowflake and Koch anti-snowflake lies in the fractal generation process. Koch anti-snowflake is the opponent of Koch snowflake. The main step of the generation process is done to develop the Koch snowflake and Koch anti-snowflake function formulas, followed by iterations. The making of the batik motif is originally carried out traditionally, which has disadvantages in terms of time and cost. However, this study proposes that the motif of batik Jlamprang can be designed mathematically with the help of Desmos software. This will definitely shorten the production time and reduce production costs. The Desmos software was chosen because it has several advantages, including easy to operate via a mobile phone or a computer. This paper examines the function formulas, iterations, and application of Koch snowflake and Koch anti-snowflake fractal geometry in designing batik Jlamprang assisted by Desmos. The method used was literature review by collecting several relevant sources. The fractal generation process produced the function formulas of Pn (perimeter) and An or Sn (area) which are necessary for designing the batik Jlamprang motif. The visualization process was carried out on Desmos, followed by geometric transformation and cloning to produce the batik Jlamprang motif as desired.