An Application of Mathematical Tessellation Method in Interior Designing

Tessellation is an arrangement of closed shapes that completely cover the plane without overlapping or leaving gaps. Escher's tessellation artworks are creative figures in the 2D plane. Tiling is a very common way in general architecture. Tilings appear in all our surroundings, i.e., floor tiles, walls, ceilings, separators and even surfaces of equipment. An aplication of tessellation in interior designing is accepted as a decorative work. For example, floor tiles could exactly be an Escher's tessellation artwork as in John August's Gecko Stone. The overall objective of the study is to emphasize how the use of interior design and different scientific disciplines could get a wealth to a place, how the situation activate the psychological perceptions and importance according to compliance with human-object-surrounding. In the present study we will try to extend Escher's tessellation artworks into 3D for interior designing. Various different textures will be gained to tessellate figures by mathematical transformations including translation, rotation, reflection and glide reflection on a surface.