Ethnomathematics: The exploration of fractal geometry in Tian Ti Pagoda using the Lindenmayer system

This study explores the concept of fractal geometry found in the Tian Ti Pagoda. Fractal geometry is a branch of mathematics describing the properties and shapes of various fractals. A qualitative method with an ethnographic approach is used in this study. Observation, field notes, interviews, documentation, and literature study obtained research data. The observation results were processed computationally using the Lindenmayer system method via the L-Studio application to view fractal shapes. The results show that the concept of fractal geometry is contained in the ornaments on the Tian Ti Pagoda. The length and angles of each part of the ornament influence the fractal shape of the Tian Ti Pagoda ornament. In addition, the length and angle modifications resulted in several variations of the Tian Ti Pagoda fractal. The findings from this study can be used as an alternative medium for learning mathematics lectures, especially in applied mathematics, dynamical systems, and computational geometry

Ethnomathematics: Exploration of Fractal Geometry in Gate Ornaments of the Sumenep Jamik Mosque Using the Lindenmayer System

Jamik Sumenep Mosque, a heritage site of the Sumenep Kingdom, was built to emphasize the acculturation of Chinese, Islamic, and Madurese cultures. This ethnomathematics research aims to reveal and explore the fractal geometry forms in the gateway of Jamik Sumenep Mosque. This study employed qualitative methods with an ethnographic approach. Research data were gathered through observation, field notes, documentation, interviews, and literature studies. Field observations were computationally analyzed using the Lindenmayer system through the L-Studio application to examine fractal shapes. The study found that the length and angle size of the ornamental parts form the basis of fractal geometry in the mosque gateway's ornamentation, thereby confirming the presence of fractal geometry concepts. These findings can be utilized in teaching fractal geometry, applied mathematics, and computational geometry. Further research could explore non-Euclidean geometry methods, such as stochastic L-system methods

ETHNOMATHEMATICS: EXPLORATION OF FRACTAL GEOMETRY IN GATE ORNAMENTS OF THE SUMENEP JAMIK MOSQUE USING THE LINDENMAYER SYSTEM

Masjid Jamik Sumenep menjadi salah satu masjid peninggalan Kerajaan Sumenep yang dibangun dengan menitikberatkan pada akulturasi budaya Tionghoa, Islam, dan Madura. Tujuan dari penelitian ethnomatematika ini yaitu untuk mengungkap dan mengeksplorasi bentuk geometri fraktal pada gapura Masjid Jamik Sumenep. Penelitian ini menggunakan metode kualitatif dengan pendekatan etnografi. Data penelitian diperoleh dengan observasi, catatan lapangan, dokumentasi, wawancara, dan studi literatur. Hasil observasi lapangan dianalisis secara komputasi menggunakan lindenmayer system melalui aplikasi L-Studio untuk melihat bentuk fraktal. Hasil penelitian menunjukkan bahwa ukuran panjang serta besar sudut pada bagian ornamen menjadi dasar pembentuk geometri fraktal dalam ornamen gapura masjid. Dengan demikian terdapat adanya konsep geometri fraktal pada ornament gapura masjid. Temuan ini dapat dimanfaatkan dalam pembelajaran geometri fraktal, matematika terapan, dan geometri komputasi. Penelitian lanjutan dapat dilakukan dengan metode geometri non euclid, seperti metode stokastik L-system

Inferring Different Types of Lindenmayer Systems Using Artificial Intelligence

Lindenmayer systems (L-systems) are a formal grammar system which consist of a set of rewriting rules. Each rewriting rule is comprised of a symbol to replace (predecessor), a replacement string (successor), and an optional condition that is necessary for replacement. Starting with an initial string, every symbol in the string is replaced in parallel in accordance with the conditions on the rewriting rules, to produce a new string. The replacement process iterates as needed to produce a sequence of strings. There are different types of L-systems, which allow for different types of conditions, and methods of selecting the rules to apply. Some symbols of the alphabet can be interpreted as instructions for simulation software towards process modelling, where each string describes another step of the simulated process. Typically, creating an L-system for a specific process is done by experts by making meticulous measurements and using a priori knowledge about the process. It would be desirable to have a method to automatically learn the L-systems (the simulation program) from data, such as from a temporal sequence of images. This thesis presents a suite of tools, collectively called the Plant Model Inference Tools or PMIT (despite the name, the tools are domain agnostic), for inferring different types of L-systems using only a sequence of strings describing the process over some initial time period. Variants of PMIT are created for deterministic context-free L-systems, stochastic L-systems, and parametric L-systems. They are each evaluated using existing known deterministic and parametric L-systems from the literature, and procedurally generated stochastic L-systems. Accuracy can be detected in various ways, such as checking whether the inferred L-system is equal to the original one. PMIT is able to correctly infer deterministic L-systems with up to 31 symbols in the alphabet compared to the previous state-of-the-art algorithm's limit of 2 symbols. Stochastic L-systems allow symbols in the alphabet to have multiple rewriting rules each with an associated probability of being selected. Evaluating stochastic L-system inference with 960 procedurally generated L-systems with multiple sequences of strings as input found the following: 1) when 3 input sequences are used, the inferred successors always matched the original successors for systems with up to 9 rewriting rules, 2) when 6 sequences of strings are used, the difference between the associated probabilities of the inferred and the original L-system is approximately 1%. Parametric L-systems allow symbols to have multiple rewriting rules with parameters that get passed during rewriting. Rule selection is based on an associated Boolean condition over the parameters that gets evaluated to choose the rule to be applied. Inference is done in two steps. In the first step, the successors are inferred, and in the second step, appropriate Boolean conditions are found. Parametric L-system inference was evaluated on 20 known parametric L-systems. For 18 of the 20 L-systems where all successors were non-empty, the successors were correctly identified, but the time taken was up to 26 days on a single core CPU for the largest L-system. The second step, inferring the Boolean conditions, was successful for all 20 systems in the test set. No previous algorithm from the literature had implemented stochastic or parametric L-system inference. Inferring L-systems of greater complexity algorithmically can save considerable time and effort versus constructing them manually; however, perhaps more importantly rather than relying on existing knowledge, inferring a simulation of a process from data can help reveal the underlying scientific principles of the process