Let’s use contemporary science & math to enjoy the Indonesian traditional & ancient batik!
delivered in International Math & Science Camp
Sari Ater, Lembang, November 24th 2011
Who doesn’t want the most playful toys, the kindest friends, the most caring and understanding teachers? It is human to look for ideal things. Things are expected to be simpler and life would be happier if we can reach out for the ideals. Even scientists, philosophers, and artists from the ancient time in northern hemisphere of our planet, creates some kind of “ideal things” while observing nature. Thus, we based our today science upon geometry. In classical geometry, we are taught to think about the perfect circle, rectangle, and a lot of excellences of geometrical shapes, upon which we put our methodological attention to nature. However, our civilization to day has forced us to accept a bad news: there is NO such “ideal things” in reality! Interestingly, we have seen this kind of point of view in some cultural heritages from ancient times in Indonesian archipelago, as well as other eastern culture rooted in ancient times!
No, there’s no such thing as perfect circle, squares, et cetera. The sciences at the end of the 20th century have witnessed that regularities are not there, in things we observe every day. We are not living in the fairy tale where things are perfect. This is a bad news for those who childishly see the reality as nightmare and keep dreaming in the world of excellences. However, this is a challenge for those who think that life is as what it is. For the beauty of our natural and social life is not within the regularities, but the irregularities, chaos, disorderliness, and how all things are kept in balancing harmony. Mathematically, it is stupid to think that the uniform, regular, normal, and order as the ideals. There is no ideals can be built, but from the reality as we perceive!
Take a look at the map of the Java Island here:
We know that the picture of an island is made of coastlines separating the land and the ocean. Now, imagine you measure it with a ruler of a meter long and then get a certain measurement.
What if on the next time, you measure it with a centimeter long ruler? Which measurement would give you a larger measurement? Since the coastline is jagged, you could get into the nooks and crannies better with the meter long ruler, so it would yield a greater measurement.
Now, imagine what if you measure the coastline with a millimeter long ruler? You could really get into the teeniest and tiniest of crannies there. Thus, the measurement would be surprisingly even bigger. You could measure it with shorter and shorter rulers, and the measurement would get longer and longer. You could even measure it with infinitesimally short rulers, and the coastline would be infinitely long! 
So that is the geometry of the nature. That’s fractal! The shape of parts of the coastlines cannot be reduced into such an “ideal” thing like “straight lines”. The “disorder” nooks and crannies are the shape of things we found on every aspect of natures: clouds are not spheres, mountains are not cones, nor does lightning travel in a straight line!  Unlike conventional geometry, fractal expresses the shape of things within its irregularities: the dimension is not 1, 2, 3, but it may be, for example, between 1 and 2 (between the shape of a line and a two dimensional space).
Yet, the ancient geometry has become the very foundation of our modern school of thought. It is interesting to discover that some aspects in the diverse cultural heritages in eastern parts of the world are not built based on the ideals, just like the geometry has built magnificent modern culture and civilization. For example, how do you think people at ancient times, lack of standard measurement tools, lack of complex mathematical abstractions, could built such a giant building like Borobudur Temple – a giant temple as magnificent as giant skyscrapers we see in town? Or how is it possible at all, ancient Javanese people created such a complex drawings in the traditional fabric of “batik” without such a sophisticated school of geometry – an attractive drawings that can be as mysterious as Michelangelo’s painting in the Sistine Chapel? 
By reading the contemporary geometry today, we can say that those people might have employed the “fractal designs” within their works. By observing thousands of the traditional “batik motif” from indigenous people in Indonesia, it is interesting to discover that they are not made based on a kind of geometrical plans and techniques that commonly used by most of us today.
Fractal is roughly the mathematics used in order to capture the dynamical aspects within nature. It is interesting to experience the fractal geometry to observe the traditional (and even the ancient) cultural heritages, of which the heterogeneity are mostly celebrated here in the archipelago of Indonesia.
When the ancient Javanese want to tell the moral story about the “self-determination on the goal of life”, they symbolized it with the bird flying, but they’re not drawing the birds as we commonly do now. They drew the flapped wing, by picturing wings, in which we could observe the smaller and transformed wings within.
When they want to tell the story about the rainy weather, which is good for farming, they symbolized it by drawing clouds. Yet, they draw the clouds, in which we can see smaller and transformed clouds within. The idea is just perfectly the same as we can see the jagged lines in the coastline that is formed by other similar (but smaller and transformed) jagged lines as we use smaller scale of measurement.
When the ancient people do not have such complex measurement scales and tools, they still could create a very complex and beautiful patterns as modern people like us frequently astonished for the awesomeness and beauty. Indonesian people wearing “batik” in social ceremonies and occasions are always a unique view for the attractiveness of the motifs and colors. Now we know that they use a kind of geometry that is not common today. They have compensated the lack of modern tools with their own “geometry” for creative designs, and today, mathematically we say that they have used the “fractal geometry”!
The modern mathematical and scientific tools have demonstrated a new kind of appreciation to the traditional and ancient cultural heritage!
 Mandelbrot, B. (1982). Fractal Geometry of Nature. W. H. Freeman.
 Peitgen, H-O., Jürgens, H., Saupe, D. (1991). Fractals for the Classroom, Part 1: Introduction to Fractals and Chaos. Springer.
 Situngkir, H. & Dahlan, R. M. (2008). Fisika Batik: Jejak Sains Modern dalam Seni Tradisi Indonesia. Gramedia.