As a a legacy from the greatness of the past, there have been still a lot of mysteries behind the structures of Indonesian Borobudur Temple. Some of them are described eloquently in Miksic (1990: 44-46). The hypothetical propositions backed by science are still a few, especially when it is related to mathematical one. Yet, Borobudur has been worldly recognized as one of biggest wonders in human civilizations. The Borobudur was a built in the theological tradition from 760 to 825 AD Mahayana Buddhist, located in Magelang, Central Java, Indonesia. Glance view of the Borobudur brings us to see the complexity of architectural design implemented to the temple with specific and unique appearance relative to other architectural and historical wonders, e.g.: Egyptian and Mayan Pyramid, Cambodian Angkor Wat.
The temple is built upon 123 x 123 m2 land and comprises 6 square platforms and 3 circular platforms on top with a dome as the highest points. The decoration of the temple presents 2,672 detail relief panels narrating Buddhist mythologies. There are 504 Buddha statues in Borobudur and various stupas, the Buddhism related mound-like and bell-shaped structure. At the circular platform of the temple, there are 72 Buddha statues seated inside perforated stupa. A description related to history of reconstruction, site description, anthropological and archaeological perspective of the site are elaborated in Soekmono (1976) as the temple is closely related to Indonesian social living, even at the modern times (Vickers, 2005). It is also worth to note a good introduction the functional part of temples, in general , in Indonesian culture as described in Soekmono (2005). The late traditional kingdoms in Indonesian archipelago inherited various temples, and Borobudur is one of the greatest.
In the other hand, by the end of the previous millennium, a lot of works and researches have shown conjectures not to approach traditional culture by using conventional geometry. The geometry of fractal (Mandelbrot, 1983) has opened the door to see traditional cultures in the fractal perspective. The work of Elgash (1999), for instance, discusses how traditional ethnic groups in Africa build the fractal structure of architectures and in other crafts. The work of Wolfram (2002) has shown some alternating point of view on traditional of Eastern cultures and recently even put foundations to algorithmic architectural studies by incorporating cellular automata. In Indonesia, explanation of fractal geometry on traditional motif of fabric, batik, has even brought to implementation of generative art of batik (Situngkir, 2008). As related to the complexity studies, fractal geometry have provided us with a way reading the complexity emanated from aspects of Indonesian traditional culture – as to the archipelago is one of the richest place with diverse ethnicities (cf. Situngkir, 2005).
The mathematical study for Borobudur’s architectural design has once related to answer the question about the metric system used by ancient Javanese to build such giant buildings with good measurement. While the anthropological revealed that Javanese used tala system (metric system with length measurement defined as the length of a human face from the forehead’s hairline to the tip of the chin or the distance from the tip of the thumb to the tip of the middle finger when both fingers are stretched at their maximum distance), the survey as elaborated in Atmadi (1988) showed there is a ratio used between parts of Borobudur. There is part of Head : Body: Foot (9 : 6 : 4) that is met in horizontal and vertical measurement of the temple. This is shown in figure 2. Furthermore, this study is related to Buddhism cosmology as shown in Long & Voute (2008). The latest showed how the temple is not only related to religious meaning, but also ancient astronomy.
Glance observation to Borobudur, we can see some apparent aspects of self-similarity – a foundation of the fractal geometry. As the shape of stupa is presented in any view as main elements of the temple, some observers sometimes see the Borobudur itself as a giant stupa. The paper is motivated by the incorporation of fractal geometry to see the architectural design that would expect more progress on revealing some interesting facts of Borobudur related to fractal geometry. The paper is constructed as follows. The next section discusses some aspects of self-similarity and fractal geometry in the Borobudur architectural design. This is followed by some discussions on the geometry of stupa as the elements of the temple. The paper ends with some further works and concluding remarks.