Exploring Homeomorphism in Building Plans

Abstract

This paper discusses a type of graph called “homeomorphically irreducible tree” (HIT) and its applicability for a formal study of symmetry in building plans. As a theoretical introduction, the mathematical properties of HITs are introduced through different historical building samples all of which display symmetry, proportion and homologous wings in their formal organization. The extracted principles are used to formulate a generative algorithm that reduces graph complexity to simple sequential numeric representation. This method is converted to a “homeomorphic machine” that is explored through generative plans. The aim of the paper is to introduce a new graph-based approach for potential morphological research into architectural symmetry. © 2020 Society for Modeling & Simulation International (SCS) centered on the notion of symmetry and branching morphogenesis in architecture. The aim of the research is two-fold. Firstly, formal computation is considered within a historical continuum where it can be applied to a broader class of historical works of architecture, potentially drawing links between them. This also requires a re-evaluation of core architectural principles such as symmetry and proportion that can potentially remedy architecture’s relationship with natural sciences. Secondly, computational methods need to be formulated primarily according to architectural principles that can overlap with various mathematical and algorithmic applications while conforming to the historical development of architectural knowledge. This aspect can have both theoretical and practical implications to architectural research and influence the formulation of new methods for machine learning in the future.