FRACTARIUM Interactive Observatory for Mathematical and Emergent Phenomena
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OBSERVATION CHAMBER / MVP

4D Shadow Projector

Rotate higher-dimensional shapes and watch their shadows fold across the screen.

dimension Operational

OBSERVATION GUIDE

Touchpoints for Observation

Observe higher-dimensional forms as rotating shadows, slices, and changing projection depth.

  • Change rotation, projection, and slicing to compare how one form casts several visible shapes.
  • A small rotation can change the shadow strongly.
  • Slicing reveals structure that projection alone hides.

This is a projection model, not a formal geometry solver.

Runs inside the browser with no upload and no registration.

SYSTEM NOTE

p = (x, y, z, w). Rotation and projection turn higher-dimensional form into a visible shadow.

OBSERVATION POLICY

This observation LAB runs in your browser. It does not upload images, pointer traces, or input.

Continue observation through connected systems.

FRACTAL Fractal Zoomer Space / Recursive Structure CHAOS Chaos Map Lab Time / Bifurcation FIELD Flow Field Painter Flow / Field WAVE Resonance Tuner Wave / Resonance NETWORK Slime Route Builder Network / Emergence ECOSYSTEM Ecosystem Balancer Life / Drift ORBIT Gravity Slingshot Orbit / Gravity
CURRENT 4D Shadow Projector Dimension / Projection
CELL Cell Rule Playground Cell / Pattern EQUATION Equation Motion Engine Equation / Motion BRANCH Decision Collapse Tree Branch / Collapse COMPLEX Complex Function Warper Complex / Mapping PROJECTION Sphere-to-Plane Mapper Projection / Sphere HYPERBOLIC Infinite Tile Disk Hyperbolic / Tiling ECHO Mutation Chain Lab Echo / Inheritance SWARM Swarm Rule Mixer Swarm / Emergence INK Ink Plume Tank Ink / Diffusion REACTION Pattern Chemistry Lab Reaction / Pattern GROWTH Particle Branch Builder Growth / Aggregation DISCHARGE Lightning Generator Discharge / Branching CRITICAL Avalanche Sandpile Criticality / Avalanche PULSE Pulse Route Network Signal / Pulse THRESHOLD Threshold Grid Threshold / Connectivity LENS Gravity Lens Warper Lens / Light KNOT Knot Crossing Inspector Knot / Invariant PHASE Phase Transition Furnace Phase / Order TERRITORY Territory Splitter Territory / Distance MAGNETIC Magnetic Field Sandbox Magnetic / Polarity SYMMETRY Symmetry Copy Maker Symmetry / Orbit INTERFERENCE Wave Interference Basin Wave / Interference GRAMMAR Rule-Grown Garden Grammar / Growth GAP Prime Gap Constellation Prime Gap / Density MODULAR Modular Domain Explorer Modular / Fundamental Domain RADON Projection Scanner Radon / Reconstruction CRYSTAL Crystal Growth Furnace Crystal / Growth VORTEX Vortex Flow Mixer Vortex / Flow NEURAL Neural Pulse Network Neural / Reroute IMMUNE Virus Defense Arena Immune / Defense RESISTANCE Flow Tank Lab Flow Tank / Wake FLOW Obstacle Flow Lab Grid Flow / Solid Mask FLOW Karman Vortex Tank Cylinder Wake / LBM FLOW CFD Solver Lab Pressure / Projection CANDIDATE AI Word Flow Words / Candidate Competition COMPLEX Riemann Sheet Navigator Complex Path / Monodromy SPECTRUM Spectral Drum Membrane / Eigenmodes TOPOLOGY Topology Flood Persistence / Connectivity OPTIMIZATION Optimal Transport Workbench Mass / Global Allocation MONODROMY Polynomial Root Braid Comparator Root Paths / Order STRUCTURE P-adic Lift Tree P-adic / Lift Tree GEOMETRY Elliptic Curve Group Law Elliptic Curve / Group Law STRUCTURE Lattice Reduction Forge Lattice / Basis HYPERBOLIC Hyperbolic Isometry Studio Hyperbolic / Isometry TROPICAL Tropical Curve Balancer Tropical / Balance HODGE Hodge Decomposition Workbench Cochain / Hodge TIME / SYNCHRONIZATION Temporal Entrainment Chamber Time / Synchronization CAUSALITY / LIGHT CONE Causal Cone Observatory Causality / Light Cone TIME / SYNCHRONIZATION Distributed Clock Network Time / Synchronization TIME / ALIASING Temporal Aliasing Observatory Time / Aliasing TIME / SYNCHRONIZATION Collective Synchronization Transition Field Time / Synchronization PROBABILITY / DIFFUSION Random Walk Diffusion Field Probability / Diffusion OPTICS / DISPERSION Prism Dispersion Observatory Optics / Dispersion LIGHT / TRANSPORT Radiance Cascade Light Transport Field Light / Transport GEOMETRY / FRACTAL VOLUME Sierpiński Tetrahedron Observatory Geometry / Fractal Volume FLOW / ADVECTION Volumetric Advection Field Flow / Advection GEOMETRY / HARMONICS Spherical Harmonic Surface Observatory Geometry / Harmonics WAVE / DISPERSION Spectral Wave Surface Field Wave / Dispersion DYNAMICS / PHASE SPACE Symplectic Map Phase-Space Observatory Phase Space / Area-Preserving Map GEOMETRY / CURVATURE Discrete Curvature Mesh Observatory Geometry / Curvature STRUCTURE / GRAPH DIFFUSION Graph Spectral Diffusion Field Graph / Diffusion STRUCTURE / DENSITY GEODESIC Optimal Transport Density Geodesic Observatory Density / Wasserstein Geodesic STRUCTURE / DIFFRACTION Quasicrystal Diffraction Observatory Quasicrystal / Diffraction SCALE / RENORMALIZATION GROUP Renormalization Flow Observatory Scale / Renormalization Group FIELD / EIKONAL WAVEFRONT Eikonal Geodesic Wavefront Observatory Field / Eikonal Wavefront QUANTUM / HOLONOMY Berry Phase Holonomy Observatory Quantum / Holonomy CRITICAL POINT / LEVEL SET Morse Landscape Observatory Critical Point / Level Set CATASTROPHE / EQUILIBRIA Catastrophe Surface Observatory Catastrophe / Equilibria NOETHER / CONSERVATION Noether Symmetry Conservation Observatory Noether / Conservation MODULAR / FAREY TESSELLATION Modular Geodesic Tessellation Observatory Modular / Farey Tessellation WAVE / NONLINEAR DISPERSION Soliton Scattering Field Wave / Nonlinear Dispersion STRUCTURE / RANDOM GRAPH Random Graph Giant Component Observatory Structure / Random Graph DEFECT / WINDING Topological Defect Winding Observatory Defect / Winding STRUCTURE / CATENARY EQUILIBRIUM Catenary Chain Observatory Static Equilibrium / Catenary STRUCTURE / CAPILLARY BALANCE Capillary Rise Observatory Surface Tension / Capillary Balance PARTICLE / TRACK VISIBILITY Cloud Chamber Track Observatory Particle / Track Visibility FIELD / PHOTOELASTIC STRESS Photoelastic Stress Observatory Field / Photoelastic Stress DYNAMICS / POINCARé SECTION Double Pendulum Poincaré Observatory Dynamics / Poincaré Section QUANTUM / TUNNELING Quantum Tunneling Observatory QUANTUM / TUNNELING GEOMETRY / MINIMAL SURFACE Catenoid Minimal Surface Observatory GEOMETRY / MINIMAL SURFACE LATTICE / BAND GAP Phononic Band Gap Observatory LATTICE / BAND GAP OPTICS / DIFFRACTION Fresnel Diffraction Observatory OPTICS / FRESNEL DIFFRACTION DYNAMICS / BILLIARD Dynamical Billiard Observatory DYNAMICS / BILLIARD STOCHASTIC / ESCAPE Kramers Escape Observatory STOCHASTIC / ESCAPE

This chamber belongs to Structures & Symmetries.

STRUCTURE Back to Structures & Symmetries Route.