House II version B, Endless House:
 -X, X -Y, Y -Z, Z

TYPOLOGY displaced through TOPOLOGY

House II version B is a house project that integrates multiple architectural typologies within a single tri-fold-topology. House II B develops multiple topological displacements layering information parametrically, combining different source codes through multiple interfaces. House II displaces multiple typologies within a unifying continuous topology. The house initially proposes three distinct programmatic areas with independent access that are then displaced and topologically integrated into a single multidimensional space. This new multi-dimensional space integrates interior and exterior intermediate spaces in a singular looping differentiated structure. This continuous tri-fold-topology simultaneously integrates into a single gradating differentiated space, both positive and negative sides of each of the three Cartesian referential axes, XYZ.  Each of the three planes (XY, ZY, ZX) proposes an initial nine square grid organization that displaces through cotinuity center and corner conditions. For instance, the corner space of the XY plane by spiraling and turning becomes continuous with the center of the YZ plane. Likewise, the courtyard space of the XY plane becomes continuous with the corner of the ZX plane (the tower type of the XYZ Cartesian Coordinate). Ultimately the center of the XZ plane becomes continuous with the perpendicular corner of the ZY plane. Therefore these displacements happen in each of the three Cartesian planes (XY,ZY,ZX) and in relation to each other's perpendicular planes, making each of the discrete planes dependent on each other, as each corner becomes the center of the other perpendicular plane.

These center-corner continuities transform structurally the overall three dimensional diagram, relating relative displacement to a structural transformation of the total project. The initial XYZ axis is overcome as an origin to the project by developing a space that displaces its own parameters since positive and negative sides of each of the Cartesian planes are integrated in a continuity, developing a multidimensional space.

Cartesian Space and Multidimensional displacement

Cartesian space has been the dominating paradigm for spatial reference and containment in architecture. Its stability has never been challenged as a system of reference. This Cartopological space displaces the three axes of its Cartesian reference space in a two fold topology per axis. By integrating negative and positive sides of each Cartesian reference plane this space displaces through a single surface the three axes of its Cartesian reference space. 

Multi-dimensional SPACE CONCEPTION

How many types of spaces architecture has ever proposed? How many spatial dimensions can architects propose to both visualize, understand and work with? How do spatial types inform spatial containment and inhabitation typologies? Spatial multi-dimensional exploration has been the area of study of mathematicians, physics and other scientists, while architects incorporate external to the discipline novel concepts and investigations to develop an architecture with interdisciplinary extrinsic content. Cartopological space proposes to invert this exchange of information. The challenge is that by exploring means to displace and challenge architecture's referential metastructure, architecture may be able to inform science.

TOPOLOGY AS SPACE-ENVIRONMENT

House IIB is also in:formed by environmental pressures. House IIBís topology is not only informed by geometric self intersection but also by a definition of a spatial differentiation based on environmental forces and fluid dynamics. Fluid dynamics inform the formal spatial progressive non-conceptual differentiation of the house by understanding space as a dynamic environment. By defining a variable space, the house does not understand any longer topo-logos as a differentiated topography only, but a topo-logos informed also by air, fluid dynamics and temperature pressures. The enfolding of the expansion of the discipline defines an object-building qualifying a multidimensional space-environment.

House II, 2013. Cartopological ©  space. Design Principal: Pablo Lorenzo-Eiroa. Research Assistant: Luo Xuan, Pedro Joaquin

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