Modular Architectural Groupings from Escher Periodic Tessellations

One of the more interesting design techniques developed by Dutch graphic artist M.C. Escher consists in covering the plane with tiles containing patterns that repeats periodically. Modularity within shape grouping is extensively used, expressed by natural figures from the living world, and also from worlds of fantasy. This paper attempts to use Eschers's ideas as a source of inspiration to obtain modular shapes to conform groups with architectural issues. The task is to satisfy design requirements and to get repeatable unitary shapes, whose geometric description is modularly manipulated within area as well as perimeter. This should be done by two procedures: 1. from the components to the whole (from the tiles to the tiling): once the designer has defined a modular constructive unit (solving a particular situation), it is possible to repeat the unit to generate modular groups, knowing that they will fit perfectly among them, without gaps nor overlaps. 2. from the whole to the components (from the tiling to the tiles): defining a tessellation with the particular rules that drives close to the architectural solution, and getting the necessary units from the tiling. There are multiple architectural themes on which this should be performed. School class-rooms, habitation buildings, shopping center sites, hotel rooms, are examples of this statement. Analyzing procedures followed by the artist, particularly those using figures that tessellate the plane periodically, we'll be able to generate tiles with architectural shape by the same way, applying different symmetry rules. Once the rules to generate shapes of tiles are known, we work within area and perimeter to satisfy modularity requirements and to convert the tiling as a geometric precise support for the insertion of architectural objects that follow predetermined dimensional patterns. In order to illustrate these ideas an example of grouping repeatable habitation units is presented