Discrete Optimization in Architecture

Quantization in Architecture & Urban Design:

1. Tessellation of space
1.1 Traditional grid/guideline systems (before the computer era)
1.1.1 Architecture
1.1.2 Urban Design

1.2 Modern (of the computer era) grid systems
1.2.1 “Collateral” systems, that is, derived from existing image pixelation
1.2.2. Space discretization serving optimization
1.2.3 Novel architectonic grid systems
1.2.3.1 Fine grid (“one cell = one agent”)
1.2.3.1.1 Agent based modeling for crowd simulation
1.2.3.1.2 Simulation in regular tessellations: Square, Triangular
& Hexagonal
1.2.3.2 Coarse grid (“cell side = minimal corridor width” )

2. Discretization of Time
2.1 The role of time in architectural (and urban design?)
2.1.1 Crowd simulations
2.1.2 Daylight simulations

3. Module as a building component
3.1 Definition of a modular system and an overview of existing modular systems
3.2. Principles of two novel modular systems: Pipe-Z (PZ) & Truss-Z (TZ)
3.2.1 Deployability of PZ & TZ

4. Bringing it all together: Overview of the cellular automaton (CA) shading as a system with discrete time
& space and realized with congruent modules.
4.1 Building Envelope and Daylighting
4.2 Why cellular automata (CA) to drive shading of building envelopes?
4.3 One-dimensional CA applied on surfaces
4.3.1 Various CA in square grid
4.3.2 Other regular tessellations: hexagonal and triangular
4.3.3 Rotating polarized film shading system
4.4 Two-dimensional CA on surfaces
4.4.1 Triangular CA
4.4.2 CA on triangulated free-form surfaces
4.5 Application of evolutionary algorithms for optimization of CA shading
4.6 Prototypes