Click nodes to propoagate. Right-click to inspect. Scroll in and out.
Click nodes to trigger proof cascades, then use the matrix to reshape the void.
Void Theorem Control Matrix
Shape propagation, bloom, and void topology in real time
Void Theorem
Interactive hypergraph proof-space where chosen axioms trigger cascading deduction paths through a living void-light topology.
OVERVIEW
Void Theorem is an interactive art system that maps formal proof structure into a navigable, emissive hypergraph. Axiom, lemma, and theorem nodes inhabit a deep procedural void; each selection propagates inference through directed hyperedges, revealing hidden theorem reachability as coherent light cascades across the graph.
ARCHITECTURE
The piece combines a typed state model for nodes and hyperedges with deterministic propagation rules and GPU-oriented rendering. Core simulation stages include topological closure, wavefront expansion, coherence/energy interpolation, and flow updates over premise-to-conclusion edges. Rendering targets instanced node geometry, flow-driven edge tubes, and an atmosphere layer that adapts to global coherence with device-tier quality controls.
FUNCTIONALITY
- Directed hypergraph core with premise sets and conclusion nodes for each inference edge
- Selection-triggered closure and BFS-style propagation front for deduction cascades
- Coherence state progression from superposition shimmer to collapsed certainty
- Energy decay and activation rules that create visible proof storm and dead-end dimming behaviour
- Flow-weighted edge styling where brightness and radius encode proof-path throughput
- Frame-rate-safe animation loop using capped delta-time updates
- Force-directed 3D layout with damping and theorem-centrality bias
- Responsive rendering tiers for desktop/tablet/mobile with explicit degradation strategy
HOW IT WORKS
Selecting a node marks it as visited and seeds a propagation front from topological reachability. On each frame, active nodes lerp toward collapsed coherence while unvisited regions oscillate in low-coherence shimmer. Hyperedges activate once premises are satisfied, then update flow intensity based on selected proof-path pressure. Camera orbit and dolly controls expose structure at macro and micro scales while preserving deterministic update order.
OUTCOMES
- Turns abstract logic and proof dependency into an explorable spatial narrative
- Demonstrates integration of graph algorithms, animation systems, and GPU-minded rendering patterns
- Introduces a distinct mathematical art piece that complements existing chaos and shader projects
- Provides a clear progress model through global coherence and reachability illumination
- Extends the portfolio with a high-concept interactive system rooted in formal structures