Expansion of parametric analysis on William M. Pena’s programming matrix theory based on graph theory

William M. Pena described his Matrix theory, or the network information table, in 1987 in his book entitled “problem seeking”. This theory presented a mechanism for architectural programming. On the other hand, the parametric paradigm has massively addressed various aspects of architecture and criticism in the past four decades. Parametric paradigm developed from formal parametric to parametric BIM in the initial dozens and ultimately to parametric automation. Parametric automation encompasses an extensive and undeniable level in the process of architectural design and criticism. This research tries to expand the William M. Pena matrix based on the parametric paradigm and develop a parametric mechanism for complex data analysis on a very large scale to help designers and critics. In other words, this research is trying to expand Pena’s theory in the context of the parametric paradigm by defining variables and facilities today so that it can serve as a model to guide the design process and criticism to architects and designers.

With the help of triple coding, Strauss’ and Corbin’s grounded theory has provided the research platform. In the following, graph theory has been used as a parametric analysis mechanism under the Gephi-version 0.9.2. The research steps are 1- Selection of the Pena Matrix and its expansion. 2- Completing content related to each cell of Matrix base and one-way communication of cells. 3- Referring the information to the team of experts for review 4- Achieving theoretical saturation measure. 5. Transfering information to Gephi software. 6-Preparation of required outputs using multiple software filters. 7- Analysis of outputs in line with the answer to the research question.

The output facilities in the Gaffe program are the degree of nodes, the weight of the vectors, the index nodes, and the shortest path between the two specified nodes, which the filters can access in the Gaffe program. On the other hand, two basic data were obtained based on the collected questionnaires. First, the one-way communication of each matrix item and then the weight of each of these communications. In order to obtain the results, the information was transferred to the Gephi program. At first, the edge weight filter, which is one of the filters of the Gephi program, was implemented on the extractive data. (These filters are based on the mathematical theory of graphs for specific outputs and standard graph theory in the program). It is possible to display only the communications of matrix cells located in this range by specifying the desired range Using app filters. As a result, more accurate and quality categorization will be possible even in countless matrix cells altogether. This mechanism also applies to the direction of another filter called grade. The degree in the theory of graphs refers to the number of connections entered and exited to each node. In this stage, the graph can be investigated based on the number of vectors entered on the base matrix cells. Finally, by citing the order of our shortest distance between the two nodes, nodes and their communications can be achieved at this stage. The output will be obtained based on node analysis and communication between them. This is precisely one of the most widely used practices of graph theory. Repeating this command in the program makes it possible to get the shortest route between the first cell in the first row and the fifth cell in all rows.

Based on codings, cells with a greater degree and weight in the defined range and the shortest distance between the two cells and related graphs are drawn. With repetition of this stage, the ability to analyze, including a comparison of frequency and analysis of alternatives, will be possible. The graph drawn in the Gephi software will determine which content exactly defined in the Matrix cells will play a role in connecting the cells of the first columns to the cells of the fifth columns and will determine the shortest communication path between them. In other words, the mechanism designed firstly, like an initial index, will play a role in the collective concept of information, and parametric analysis of unidirectional communication between Matrix cells will be able to analyze communication on a macro scale. These analyzes are available to designers graphically and parametrically. By changing each parameter or basic communication, the ability to analyze and compare changes to the word humanity will be provided. As a result, by reference to the research question, this parametric mechanism based on William M. Pena’s matrix theory with multiple accurately adjustable outputs in the Gephi program will be able to first create a parametric structure and simply observe and compare the changes in the output graphs by changing the basis information. As a guide, it will also determine the path of the required data and communication and open the path to design and criticism.