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K e y w o r d s : Parametric designing; Intense single-family housing; Numerical parameters of single-family housing; Smart cities; Compact city. T . B r a d e c k i , D . K ą t n y mendations, standards or experience. Nowadays, such an approach may be supplemented by creating housing scenarios using parametric tools. Parametric specification originates from mathematics, where certain parameters, i.e. variables, may be edited to manipulate the final result of an equation or system of equations. An example of such a parametric equation is presented in the study by professor Leszek Mieszkalski who developed the formula for mathematical modeling of potato tubers [4]. Patrik Schumacher, who cooperated with ZahaHadid, claims that parametric designing is not only the method of creating complex geometries, but also the next big step in architecture. In his opinion, it would be justified to introduce a new, global style, both in architecture and urban planning: parametricism [5]. A critical opinion on that movement and the possibilities to use it, were presented, among others, by Michał Stangel who considered it promising, but also bearing certain drawbacks [6]. Its application in designing cities is quite beneficial, as it allows to create a flexible structure that may be changed quickly and effectively, depending on designer’s preferences or various conditions, which allows one to arrive at different results while starting from the same original idea. Also, this allows to adapt the project to new problems that appear over time during development of the urban fabric [5]. Other designers also emphasize the significance of parametric techniques in designing the so-called smart cities. They are characterized by much greater efficiency at lower consumption of resources. For that purpose, a gigantic number of factors has to be considered, analyzed, and then transformed into an urban form. The best way of resolving that problem is parametric designing [8]. Based on the broadly understood urban theory, a convenient area for the purposes of a theoretical project for a residential complex is ca. 100 ha, i.e. an area similar to a circle or square of the diameter or side equal to 1000 meters. That way of thinking was first introduced by Clarence Perry, with his theory of a neighborhood unit, which is currently disseminated and updated, among others, by Douglas Farr and Richard MacCormac. In his “Sustainable Urbanism”, Douglass Farr proposed minimum values of density to make new housing areas sustainable – he suggested that minimum rational densities should not fall below 40 apartments per hectare [7]. In turn, Richard MacCormac claims that what is rational in terms of public transport economy, is placement of 10 thousands citizens in an area of ca. 100 ha [11]. It may be assumed that the center of such an area would be equipped with a public transport stop as well as the basic facilities: a school, a preschool, a large food store, as well as a local park with a community center (cultural center or after school club). Such composition allows, in theory, to reach the center on foot (ca. 5–10 minutes) and so it is consistent with the broadly understood sustainable development movement, because it limits local trips. Among others, this is confirmed by Krystyna Solarek who stated that, despite the fast and chaotic development of cities, certain rules can be found: the main transportation routes of urban units points towards certain local center, and plot parcelling led to an octagonal mesh [9]. The following question may be asked based on the above-mentioned assumptions: In our times, is it possible to develop a properly compact single-family housing complex which, on the one hand, addresses the community needs of high quality of life and, on the other, meets the premises of properly dense housing? In order to answer that question, the authors decided to use the parametric method for simulation of housing variants.

Compact Single-Family Housing Generated by Parametric Design – Search for Optimal, Sustainable or Smart Densities