Tzu-Chieh Kurt Hong, PhD

Assistant Professor
School of Architecture and Design
University of Kansas, Lawrence KS

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Herds of Architecture I

Enumerations of Two Tetris Blocks

Georgia Institute of Technology
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 ):