Harmony of the World: Reliving Johannes Keppler Legacy
The motif is inspired by the traditional Indonesian Kawung pattern, which is tessellated using semiregular tessellation. There are eight semiregular tessellations, each composed of two or more regular polygons. Semiregular tessellations exhibit a harmonious combination of these polygons, creating a visually captivating and culturally rich design.
Math Concept
In this piece, the traditional Kawung pattern is generalized into an n-leaf Kawung using a simple mathematical principle involving Bezier curves. Describing a Kawung leaf using Bezier curves requires a minimum of three points: the start, mid, and end points. To create a Kawung leaf, two Bezier curves are employed. In the first curve, the journey begins at the origin, moves to the midpoint between corner 1 and 2, and concludes at corner 2. For the second curve, the starting point is corner 2, followed by the midpoint between corner 2 and corner 3, ultimately returning to the origin.
We can try to make tessellation using this interactive image below. You can click on the Kawung part to create tessellation. Try and play around with this image to build sense on how tessellation works.
How to Draw
Semiregular tessellation employs various types of polygons, including triangles, squares, hexagons , octagons, and dodecagons (polygons with 12 sides). Tutorials on how to draw each of these polygons given a specific side length can be found by clicking the link provided in this paragraph. Below is sample tutorial on how to draw three leaves kawung based on triangles:
1. Given triangle ABC with side length AB, Draw the perpendicular bisector of AB. Perpendicular Bisector is a line that exactly divides the given line segment into two congruent parts making an angle of 90 degrees with it
2. Draw the perpendicular bisector of BC.
3. Draw the perpendicular bisector of CA. The intersection of the perpendicular bisectors is the center of the circle circumscribing the triangle. This is the origin (0,0)
4. Draw the three-leaves Kawung based on a quadratic Bezier curve. Begin at the origin (0,0), use the midpoint between vertices as the control point, and the vertices as the endpoint.
Exhibit
Presenting the Dodecagon Kawung Necklace by The Geometry of Batik Team. With the mathematical model in hand, creating a 3D model becomes a straightforward process. The resulting 3D model serves as the foundation for crafting this necklace using the lost wax casting method in our exhibit