Department of Mathematics and Systems Analysis

Crystal Flowers in Halls of Mirrors


Liisi Huotari, Satu Kruus, Marloes Van Son, Siyan Zhuang


Kello / Clock expresses time by using lights and shapes. Its tessellation is composed of sixty triangles and twelve rhombs, which represent hours, minutes and seconds. By switching lights on and off, it aims to create a sense of time rather than an exact representation. Through symmetrical and asymmetrical patterns, it displays a cyclic division of time that forms the core of all clocks.
When we started designing the work, we had many different ideas, including laser polyhedra, changing shadow tilings, harmonographs, and projections. The ideas developed into a tessellated clock, for which we defined a system that determines when and how the tilings change. This piece, like any clock, divides time into equal parts. The symmetries change according to the periods of seconds, minutes, and hours. Although measurement of time is linear and fixed, perception of time is not. In our clock, each hour has a different way of changing its symmetries, sometimes clockwise, sometimes mirroring, sometimes from the center towards the edges and so on.

We considered different illuminating patterns that could be used to tell the time. We first thought about using the amount of translational and reflective symmetries to tell the time. However, to avoid obscurity, we chose to use a relatively simple system where the amount of illuminated shapes tells the time. This means that a pattern of four illuminated trapezoids represents four o’clock. Similarly a pattern of fifty illuminated triangles represents fifty minutes. This enabled us to use our imagination on the variation of illumination-patterns during each hour and from one hour to another. The composition of the minutes changes every second, and the composition of hours every minute.

The creation of Kello / Clock included many steps of planning and crafting. We started with cutting plexiglass and building a hexagonal plywood container. Inside the container, we built cardboard walls separating the areas of triangles and rhombs, preventing light to exceed the boundaries of these areas. Furthermore, we designed and implemented the patterns, soldered the LED-circuit, and programmed the clock’s internal logic with the Arduino software.

Kello / Clock as a physical object, is a hexagonal board that hangs from the wall. It is nearly 30cm thick, and nearly 170cm long in diagonals.

This project has been full-extend teamwork. We faced different kinds of challenges with logistics and materials, but we always managed to adjust our plans to the changing situation. Combining our strengths resulted in fascinating learning experiences, and we look forward to present our alternative time-expression system to a wider audience.

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