Dubai is a city of rapid urban changes, and superlative architecture. These non-incremental urban changes tend to leave large urban areas unexplored. Dubai metro line and its surrounding area is one of these sites that can be classified under Jane Jacobs' border vacuum. In this study, the authors take on the challenge of transforming a wasted area that is acting as an urban divider and turning it into a walkable, liveable and vibrant public space. This is done through two methods; one is a survey of users that focused on the measures of walkability, liveability and vibrancy. The other one is an urban design analysis of the site's urban morphology and prospects. Urban designers must acknowledge all three measures considered here in order to design context relevant and vibrant spaces.

PurposeThis research introduces a hypothesis for establishing typologies and patterns for architectural plans based on their climate, culture and orientation. The repetition and reproduction of spaces in architectural plans are rooted in mathematical equations. Factorial and permutation formulae are the type of equations used as scientific tools to define typology. In addition, a new perspective on culture and privacy in line with the Arabic house is included to illustrate the practicality of restricted plans according to cultural needs.Design/methodology/approachTo make the approach accessible, the theory is integrated into a software using C++ as the programming tool. Accordingly, all patterns and typologies are reproduced by inserting digits or numbers to simulate the process of using permutations and factorials for the creation of diagrammatic patterns and, subsequently, architectural plans.FindingsThe authors recommend that this method be integrated in future housing studies at earlier stages to obtain a high number of alternatives for architectural plans. The results of mathematical permutation of this study will help architects and designers to evolve their methods and processes through creating alternative patterns and culture (and climate)-specific typologies to provide more design possibilities.Originality/valueThis study is set to improve the adjacency diagram theory into the adjacency diagram with orientation theory, which accounts for the geographical orientation to obtain more comprehensive and climate-responsive patterns.