Research

Herds of Architecture I

Enumerations


Georgia Institute of Technology
2021
The project ‘The Herd of Architecture’ is a project of mathematical art inspired by a research work ‘The Animals of Architecture’ in the literature (March L & Martela R, 1974). In this study, the authors calculated (enumerated) all possible configurations of 6, 7 and 8 squares under a constrains that all squares are connected to one another. This project is aiming for one more step as the tribute to the authors, that is: How many animals are there if two N-ominoes are connected? In this project, we started from N=4, that is, connecting two 4-ominoes (for example, a T shape and an L shape). Instead of calculating in a mathematical way, the result is derived by implementing a shape rules to enumerate the possibilities with the removal of equivalent copies. In total, there are ten herds (families) out of five animals, that is a combinatoric claculation C(5,2)=10. Here are the enumerations of the ten families.


Herd 1 ( T + L ):



Herd 2 ( T + l ):


Herd 3 ( T + Z ):


Herd 4 ( T + □ ):


Herd 5 ( L + l ):


Herd 6 ( L + Z ):


Herd 7 ( L + □ ):


Herd 8 ( Z + l ):


Herd 9 ( Z + □ ):


Herd 10 ( □ + l ):