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Group Theory and Architecture:

The Affine Group, 1.




 
 

In his next book, Michael Leyton presents a theory of design based on Lie groups and Lie algebras. Below are shown some of the architectural designs that appear in the book. They were all generated using control-nested hierarchies of affine groups AGL(3,R). Later in this series of websites we will show examples created by tensor algebras. The illustrations below have been presented with every line visible - even lines that would be occluded by the actual building masses - in order to make the group-theoretic structure more evident. The illustrations are taken from a 3D interactive model.

Later this year, this web-site will contain a viewable tech-report summarizing the theory in the forthcoming book.
 


Click for larger, 10Kb

Clear/Lake Monastery Project - Lobby 3 [F_Lobby3]


Clear/Lake Monastery Project - Lobby View 4 [F_LobbyPlan4]


Clear/Lake Monastery Project - Lobby View 6 [F_LobbyPlan6]


Clear/Lake Monastery Project - Lobby View 5 [F_LobbyPlan5]


Clear/Lake Monastery Project - Lobby View 7 [F_LobbyPlan7]




 
 



Black-and-White Images:
 
 

Clear/Lake Monastery Project - Lobby Building, view 12. [F_Lobby12]


Clear/Lake Monastery Project - Lobby Building, view 4. [F_Lobby4]


Clear/Lake Monastery Project - Lobby Building, view 9. [F_Lobby9]


Clear/Lake Monastery Project - Lobby Building, view 10. [F_Lobby10]


Clear/Lake Monastery Project - Lobby Building, view 11. [F_Lobby11]



 
 

Professor Leyton is president of the following two societies:

International Society for Mathematical Aesthetics:
http://www.rci.rutgers.edu/~mleyton/ISMA.htm

International Society for Group Theory in Cognitive Science: ttp://www.rci.rutgers.edu/~mleyton/GT.htm
 


His homepage is http://www.rci.rutgers.edu/~mleyton/homepage.htm

Email address: MLeyton@msn.com