The math behind JA logo
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JA logo has symmetries. It is inspired by the “Kite and Dart” P2 tiling (tessellation) discovered by Nobel laureate mathematician Roger Penrose. Penrose's P2 tiling uses two quadrilaterals called the "kite" and "dart", which may be combined to make a rhombus. There are matching rules that specify how tiles may meet each other. However, the matching rules prohibit the combination of rhombus. These matching rules ensure that the "kite" and "dart" tiles tessellate the plane only non-periodically thus they create aperiodic tessellations.
JA logo creates symmetries. Celebrating our participation at the GEN-E Festival we designed and produced a Wizzle model that creates the JA logo and explores the symmetries that can be achieved by it.
With the JA logo Wizzle model we designed Season’s Greetings e-cards in collaboration with JA Europe and JA Greece.
The cards were offered for free to the educational community and the general public.
Roger Penrose in the foyer of the Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, standing on a floor with a Penrose tiling.
A tessellation is non-periodic when it does not create a repeating pattern. When a set of tiles tessellates the plane in only a non-periodic way, it is called aperiodic, and the tiling is called aperiodic.
Aperiodic tessellations constitute a very difficult and fascinating mathematical problem. This problem received a great interest in the 1960s. Mathematicians tried to find sets of tiles that tessellate the plane aperiodically. The first aperiodic tilling was obtained with a set of 20,426 tiles. Within a decade, mathematicians invented new sets of fewer and fewer tiles that create aperiodic tessellations.
In the 1970s, Roger Penrose impressed by presenting two aperiodic sets of just two tiles each, the "kite and dart" (P2) and the "rhombus" (P3). We were inspired by the "rhombus" P3 and created the Wizzle model "fish n bird" which creates a Penrose P3 aperiodic tessellation on the plane.
Penrose P1 aperiodic tessellation with a set of six tiles.
Penrose P2 (kite and dart) aperiodic tessellation
Penrose P3 (rhombus) aperiodic tessellation
"Fish n Bird" Wizzle model creates a P3 Penrose aperiodic tessellation
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