Batik Jlamprang with Koch Snowflake and Koch Anti Snowflake Fractal Geometry using Desmos

Abstract

Batik Jlamprang is a cultural heritage from Pekalongan. This batik has a round shape and floral ornaments. The motif of batik Jlamprang is similar to the Koch snowflake. Mathematically, batik Jlamprang is 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 generating process. Koch Anti-Snowflake is the opponent of Koch Snowflake. The main step of the process is generated by compiling Koch Snowflake and Koch Anti-Snowflake function formulas, followed by iteration. The making of the batik motif is initially carried out traditionally, which has disadvantages in terms of time and cost. However, nowadays, the motif of batik Jlamprang can be made mathematically with the help of Desmos software. This will definitely shorten the time and reduce production costs. Desmos software was chosen because it has several advantages, including being easy to operate via mobile phone or computer. This paper examines the function formula, iteration, and application of Koch Snowflake and Koch Anti-Snowflake fractal geometry in designing batik Jlamprang assisted by Desmos. The method used was library research by collecting several relevant sources. The generating process produced a function formula of Pn (perimeter) and An or Sn (area) which is useful for designing the motif of batik Jlamprang. The visualization process was carried out on Desmos, followed by geometry transformation and cloning that were able to produce the motif of batik Jlamprang as desired.