Pemodelan Motif Batik melalui Simulasi Numerik Persamaan Gelombang Air Dangkal Satu Dimensi

Indonesian

Abstract

This study discusses the modeling of batik motifs using a mathematical approach through numerical simulation of the one-dimensional shallow water wave equation. The problem addressed is how wave patterns generated from the equation can form visual patterns resembling batik motifs. The purpose of this research is to explore the potential of the shallow water wave equation in producing batik motif patterns mathematically. The method used is numerical simulation to solve the one-dimensional shallow water wave equation with specific initial and boundary conditions, with topographical functions b₂(x) and b₄(x) as the main reference for pattern generation. The results show that variations in wave parameters, such as amplitude and propagation speed, produce diverse patterns that resemble traditional batik motifs. The b₂(x) topographical function produces patterns with gentle and smooth characteristics, suitable for soft-toned motifs such as megamendung and lereng. Meanwhile, the b₄(x) function produces patterns with sharp and dynamic variations, suitable for parang and truntum motifs. Therefore, mathematical modeling through numerical simulation can serve as an innovative alternative for the development of batik motifs based on science and technology.