Algorithms — Phase 8 Suite

Route: /algorithms
Purpose: Execute specialist, computationally intensive AEC algorithms directly on the Purple8 Knowledge Graph to validate, optimize, and generate architectural solutions.

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1. What are the Phase 8 Algorithms?

In traditional BIM, analysis happens reactively at the end of a design phase: an architect exports a model to a structural engineer or a sustainability consultant, waits weeks for the analysis, and then retroactively fixes mistakes.

The Phase 8 Algorithms flip this paradigm. They are a suite of 12 graph-native, high-performance computational engines that run proactively and continuously. Because the building is represented as a mathematical graph (nodes and edges) rather than heavy 3D geometry, these algorithms can solve complex spatial, physical, and environmental equations in milliseconds rather than hours.

Proactive vs. Reactive Modes

• Proactive (Early design): During concept and feasibility stages, algorithms like Space Syntax and Solar Optimisation run against your sketch or room programme to surface constraints before you commit to a layout.
• Reactive (Validation): During technical design, algorithms like Structural Topology, MEP Flow, and Egress Pathfinding validate the current state of the project graph. If a layout change creates a problem, the algorithm flags it immediately.

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2. The 12 Algorithms

#	Algorithm	What it does
8.1	Space Syntax & VGA	Visibility Graph Analysis — integration scores, J-graph, axial maps. Predicts human movement, footfall, and wayfinding quality.
8.2	Structural Topology	Rigidity testing (Maxwell/Laman), load path tracing, critical member detection, Cuthill-McKee FEM ordering, truss force distribution.
8.3	IFC Change Propagation	Ingests IFC files, detects changes vs. previous version, propagates updates through the graph, runs clash detection.
8.4	Generative Design	Graph-colouring + constraint propagation for spatial allocation, egress optimisation (Dijkstra/min-cut), urban zone detection.
8.5	MEP Flow Analysis	Max-flow/min-cut (Edmonds-Karp), thermal zone simulation, energy balance, fault isolation BFS, redundancy path analysis.
8.6	Graph Grammars	Production rules with AC-3 constraint propagation — generates code-compliant plan configurations from spatial rules.
8.7	Spectral Graph Theory	Graph Laplacian, Fiedler value/vector (λ₂), spectral bisection, robustness index, natural frequency estimation.
8.8	Topology Optimisation	SIMP-on-Graph density loop — finds optimal material distribution in a structural mesh while respecting load and boundary constraints.
8.9	Multi-Objective RL	Gym-compatible environment with a GCN policy — optimises simultaneously for VGA, egress, spectral gap, and MEP max-flow. Pareto front tracking.
8.10	MPNN Physics Kernel	Message-passing neural network as a fast surrogate for FEM nodal displacement prediction — results in milliseconds instead of minutes.
8.11	Hypergraph Algorithms	Models multi-way relationships (one relationship connecting 3+ elements). Minimum transversal, Laplacian partitioning, sub-hypergraph isomorphism.
8.12	IFC Advanced Rewriting	Declarative rewrite rules applied to IFC geometry — diff_and_patch() for incremental IFC updates, conversion pipelines to VGA/structural graphs.

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Running an Algorithm

From Canvas (recommended)

The fastest way to reach a Phase 8 algorithm is directly from the Canvas drawing:

1. Draw your floor plan on Canvas
2. Press V to cycle to the relevant overlay (Space Syntax, Structural, or Zen)
3. The Analysis panel appears on the right edge of Canvas — it shows live summary metrics for that phase
4. Click Full Analysis → at the bottom of the panel

This opens the Algorithms page with the matching tab pre-selected:

Canvas overlay	Algorithm tab opened
Space Syntax	Phase 8.1 — Space Syntax & VGA
Structural	Phase 8.2 — Structural Topology
Zen	Phase 8.9 — Multi-Objective RL / Wellbeing

Press Back (or the browser back button) to return to your Canvas drawing.

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Direct access

1. Go to Algorithms in the sidebar
2. Select the tab for the algorithm you need (e.g. Space Syntax)
3. Set your Project ID in the top input field
4. Fill in any required parameters and click Run
5. Results return as JSON — metrics, pass/fail flags, and a cot_steps chain-of-thought log explaining the reasoning

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Suggested combinations

• Residential unit planning: 8.1 Space Syntax → 8.2 Structural Topology → 8.5 MEP Flow
• Commercial office: 8.1 Space Syntax → 8.6 Graph Grammars → 8.8 Topology Optimisation
• IFC import workflow: 8.3 IFC Propagation → 8.12 IFC Rewriting → 8.2 Structural Topology
• Optimisation research: 8.7 Spectral → 8.9 Multi-Objective RL → 8.10 MPNN Physics