Kolam is a ritual art form practised by people in South India and consists of rule-bound geometric patterns of dots and lines. Single loop Kolams are mathematical closed loop patterns drawn over a grid of dots and conforming to certain heuristics. In this work, we propose a novel encoding scheme where we map the angular movements of Kolam at lattice points into sequences containing $4$ distinct symbols. This is then used to simulate single loop Kolam procedure via turtle moves in accordance with the desired angular direction at specific points. We thus obtain sequential codes for Kolams, unique up to cyclic permutations. We specify the requirements for the algorithm and indicate the general methodology. We demonstrate a sample of Kolams using our algorithm with a software implementation in Python.

翻译：科拉姆是南印度人民践行的一种仪式艺术形式，由遵循规则的点和线几何图案构成。单回路科拉姆是在点阵上绘制并符合特定启发式规则的数学闭合回路图案。本研究提出一种新颖的编码方案，将科拉姆在格点处的角位移映射为包含4个不同符号的序列。进而利用该编码通过龟标移动模拟单回路科拉姆的生成过程，使移动方向与特定点处的期望角度保持一致。由此获得科拉姆的序列化编码，该编码在循环置换意义下具有唯一性。我们明确了算法要求并阐述了通用方法论。通过Python实现的软件示例，展示了采用本算法生成的部分科拉姆样本。