MAIN HALL / RESEARCH FACILITY

FRACTARIUM

Interactive Observatory for Mathematical and Emergent Phenomena

Observe. Distort. Interfere. Explore.

A quiet browser-based observatory for mathematical structures, physical patterns, fields, waves, thresholds, and emergent forms.

ENTER LAB OBSERVE SYSTEMS

Browser only.
No upload.
No installation.
No account required.

WHAT IT IS

A set of live browser observation chambers. Each LAB is a small interactive field for watching structure, motion, threshold, trace, or emergence appear on the canvas.

HOW TO TOUCH IT

Start from a chamber, then disturb the field. Switch modes, drag points, add signals, change sliders, and use REPORT or Save PNG when the current state is worth keeping.

WHAT IT IS NOT

Not a formal solver or diagnosis tool. The chambers are visual observation models. They run locally in the browser and do not require upload, account, or installation.

BOOT SEQUENCE

Observation environment is online. The browser chamber is ready. No account required.

OBSERVATION MODE

Interactive field access. Touch, drag, zoom, and save the active structure.

SIGNAL TRACE

Resonance channel released. 92 active chambers now observe space, time, flow, waves, networks, life-like drift, orbital gravity, projection, cellular patterns, equation-driven motion, branching, complex-function warping, hyperbolic space, inherited echoes, swarms, ink, reaction fields, aggregation growth, discharge paths, sandpile avalanches, pulse routes, threshold connectivity, gravity-lens warping, knot crossings, phase boundaries, territory borders, magnetic polarity, symmetry copies, basin interference, rewriting grammar, prime-gap star maps, modular fundamental domains, Radon projection fields, crystal-growth fronts, vortex mixing, neural pulse rerouting, immune-field defense, dye wake patterns inside a flow tank, solid-mask obstacles inside a grid flow field, fixed-cylinder wake alternation inside a vortex tank, weighted next-word candidate competition, Riemann-sheet monodromy, membrane spectra, topology changes, optimal transport, polynomial-root braids, p-adic lifts, elliptic-curve group laws, lattice reduction, hyperbolic isometries, tropical balancing, Hodge decomposition, temporal entrainment, causal-cone phenomena, distributed clock networks, and temporal aliasing.

ACTIVE CONNECTIONS

SYSTEM MAP

01 SPACE Fractal Zoomer 02 TIME Chaos Map Lab 03 FLOW Flow Field Painter 04 RESONANCE Resonance Tuner 05 NETWORK Slime Route Builder 06 LIFE Ecosystem Balancer 07 ORBIT Gravity Slingshot 08 DIMENSION 4D Shadow Projector 09 CELL Cell Rule Playground 10 EQUATION Equation Motion Engine 11 BRANCH Decision Collapse Tree 12 COMPLEX Complex Function Warper 13 PROJECTION Sphere-to-Plane Mapper 14 HYPERBOLIC Infinite Tile Disk 15 ECHO Mutation Chain Lab 16 SWARM Swarm Rule Mixer 17 INK Ink Plume Tank 18 REACTION Pattern Chemistry Lab 19 GROWTH Particle Branch Builder 20 DISCHARGE Lightning Generator 21 CRITICAL Avalanche Sandpile 22 PULSE Pulse Route Network 23 THRESHOLD Threshold Grid 24 LENS Gravity Lens Warper 25 KNOT Knot Crossing Inspector 26 PHASE Phase Transition Furnace 27 TERRITORY Territory Splitter 28 MAGNETIC Magnetic Field Sandbox 29 SYMMETRY Symmetry Copy Maker 30 INTERFERENCE Wave Interference Basin 31 GRAMMAR Rule-Grown Garden 32 GAP Prime Gap Constellation 33 MODULAR Modular Domain Explorer 34 RADON Projection Scanner 35 CRYSTAL Crystal Growth Furnace 36 VORTEX Vortex Flow Mixer 37 NEURAL Neural Pulse Network 38 IMMUNE Virus Defense Arena 39 RESISTANCE Flow Tank Lab 40 GRID FLOW Obstacle Flow Lab 41 WAKE Karman Vortex Tank 42 PROJECTION CFD Solver Lab 43 CANDIDATE AI Word Flow 44 MONODROMY Riemann Sheet Navigator 45 SPECTRUM Spectral Drum 46 TOPOLOGY Topology Flood 47 TRANSPORT Optimal Transport Workbench 48 ROOT BRAID Polynomial Root Braid Comparator 49 P-ADIC / LIFT P-adic Lift Tree 50 GROUP LAW Elliptic Curve Group Law 51 LATTICE Lattice Reduction Forge 52 HYPERBOLIC / ISOMETRY Hyperbolic Isometry Studio 53 TROPICAL / BALANCE Tropical Curve Balancer 54 COCHAIN / HODGE Hodge Decomposition Workbench 55 TIME / SYNCHRONIZATION Temporal Entrainment Chamber 56 CAUSALITY / LIGHT CONE Causal Cone Observatory 57 TIME / SYNCHRONIZATION Distributed Clock Network 58 TIME / ALIASING Temporal Aliasing Observatory 59 TIME / SYNCHRONIZATION Collective Synchronization Transition Field 60 PROBABILITY / DIFFUSION Random Walk Diffusion Field 61 OPTICS / DISPERSION Prism Dispersion Observatory 62 LIGHT / TRANSPORT Radiance Cascade Light Transport Field 63 GEOMETRY / FRACTAL VOLUME Sierpiński Tetrahedron Observatory 64 FLOW / ADVECTION Volumetric Advection Field 65 GEOMETRY / HARMONICS Spherical Harmonic Surface Observatory 66 WAVE / DISPERSION Spectral Wave Surface Field 67 PHASE SPACE Symplectic Map Phase-Space Observatory 68 GEOMETRY / CURVATURE Discrete Curvature Mesh Observatory 69 GRAPH / DIFFUSION Graph Spectral Diffusion Field 70 DENSITY / WASSERSTEIN GEODESIC Optimal Transport Density Geodesic Observatory 71 QUASICRYSTAL / DIFFRACTION Quasicrystal Diffraction Observatory 72 SCALE / RENORMALIZATION GROUP Renormalization Flow Observatory 73 FIELD / EIKONAL WAVEFRONT Eikonal Geodesic Wavefront Observatory 74 QUANTUM / HOLONOMY Berry Phase Holonomy Observatory 75 CRITICAL POINT / LEVEL SET Morse Landscape Observatory 76 GROWTH / CATASTROPHE EQUILIBRIA Catastrophe Surface Observatory 77 STRUCTURE / NOETHER CONSERVATION Noether Symmetry Conservation Observatory 78 GEOMETRY / MODULAR FAREY TESSELLATION Modular Geodesic Tessellation Observatory 79 WAVE / NONLINEAR DISPERSION Soliton Scattering Field 80 STRUCTURE / RANDOM GRAPH Random Graph Giant Component Observatory 81 DEFECT / WINDING Topological Defect Winding Observatory 82 STATIC EQUILIBRIUM / CATENARY Catenary Chain Observatory 83 SURFACE TENSION / CAPILLARY BALANCE Capillary Rise Observatory 84 PARTICLE / TRACK VISIBILITY Cloud Chamber Track Observatory 85 FIELD / PHOTOELASTIC STRESS Photoelastic Stress Observatory 86 DYNAMICS / POINCARÉ SECTION Double Pendulum Poincaré Observatory 87 QUANTUM / TUNNELING Quantum Tunneling Observatory 88 GEOMETRY / MINIMAL SURFACE Catenoid Minimal Surface Observatory 89 LATTICE / BAND GAP Phononic Band Gap Observatory 90 OPTICS / FRESNEL DIFFRACTION Fresnel Diffraction Observatory 91 DYNAMICS / BILLIARD Dynamical Billiard Observatory 92 STOCHASTIC / ESCAPE Kramers Escape Observatory

CHOOSE A ROUTE

Start with what you want to watch

GEOMETRY

Shape & Space For days when you want space to bend, fold, stretch, and reveal hidden structure. 19 LAB route

FIELD

Fields in Motion For watching invisible forces become trails, currents, wakes, waves, and pressure. 23 LAB route

GROWTH

Growth & Thresholds For patterns that branch, crystallize, topple, connect, melt, or grow from rules. 8 LAB route

SIGNAL

Signals & Networks For timing, rerouting, resonance, equations, chaos, and branching decisions. 16 LAB route

LIFE-LIKE

Life-like Emergence For systems that feel alive without pretending to be biology or medicine. 5 LAB route

STRUCTURE

Structures & Symmetries For borders, copies, gaps, crossings, and higher-dimensional shadows that leave structure behind. 21 LAB route

ACCESSIBLE CHAMBERS

ACTIVE SYSTEMS

FRACTAL / STATUS: ACTIVE

Fractal Zoomer

Zoom Mandelbrot, shift Julia parameters, and watch recursive coastlines unfold. INITIALIZE

CHAOS / STATUS: ACTIVE

Chaos Map Lab

Tune the logistic map and watch steady motion split into chaos. INITIALIZE

FIELD / STATUS: ACTIVE

Flow Field Painter

Choose a flow rule and release particles through spirals, streams, and attractors. INITIALIZE

WAVE / STATUS: ACTIVE

Resonance Tuner

Tune frequency, phase, and amplitude until waves lock, cancel, or stand still. INITIALIZE

NETWORK / STATUS: ACTIVE

Slime Route Builder

Place food and blocks, then watch paths reroute and fade. INITIALIZE

ECOSYSTEM / STATUS: ACTIVE

Ecosystem Balancer

Shift food, predators, and climate until populations wobble. INITIALIZE

ORBIT / STATUS: ACTIVE

Gravity Slingshot

Adjust mass and speed, then watch probes fall, escape, or whip around gravity wells. INITIALIZE

DIMENSION / STATUS: ACTIVE

4D Shadow Projector

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

CELL / STATUS: ACTIVE

Cell Rule Playground

Pick local rules and watch cells spread, drift, or die. INITIALIZE

EQUATION / STATUS: ACTIVE

Equation Motion Engine

Change equation terms and watch motion spiral, pulse, or settle. INITIALIZE

BRANCH / STATUS: ACTIVE

Decision Collapse Tree

Add pressure and noise, then watch branches grow, lock, fade, and collapse. INITIALIZE

COMPLEX / STATUS: ACTIVE

Complex Function Warper

Switch complex functions and watch grids, circles, and points bend, flip, and wrap. INITIALIZE

PROJECTION / STATUS: ACTIVE

Sphere-to-Plane Mapper

Push points from a sphere onto a plane and watch the north pole stretch toward infinity. INITIALIZE

HYPERBOLIC / STATUS: ACTIVE

Infinite Tile Disk

Warp a Poincare disk and watch hyperbolic tiles shrink toward an infinite rim. INITIALIZE

ECHO / STATUS: ACTIVE

Mutation Chain Lab

Tune mutation, memory, and selection as information strands branch and fade. INITIALIZE

SWARM / STATUS: ACTIVE

Swarm Rule Mixer

Change local flocking rules and watch groups split, scatter, align, and regroup. INITIALIZE

INK / STATUS: ACTIVE

Ink Plume Tank

Drop ink into water and watch plumes sink, curl, spread, and fade. INITIALIZE

REACTION / STATUS: ACTIVE

Pattern Chemistry Lab

Adjust feed and kill rates to grow spots, stripes, and cells. INITIALIZE

GROWTH / STATUS: ACTIVE

Particle Branch Builder

Release walkers and watch them stick into branching structures. INITIALIZE

DISCHARGE / STATUS: ACTIVE

Lightning Generator

Raise voltage, place obstacles, and watch lightning find ground. INITIALIZE

CRITICAL / STATUS: ACTIVE

Avalanche Sandpile

Drop grains until one threshold break sends an avalanche through the pile. INITIALIZE

PULSE / STATUS: ACTIVE

Pulse Route Network

Fire pulses through a network and watch delay, sync, echo, and route memory appear. INITIALIZE

THRESHOLD / STATUS: ACTIVE

Threshold Grid

Open cells until scattered islands suddenly connect. INITIALIZE

LENS / STATUS: ACTIVE

Gravity Lens Warper

Bend starlight around a heavy center and watch rings, rays, and disks warp. INITIALIZE

KNOT / STATUS: ACTIVE

Knot Crossing Inspector

Rotate a closed loop and inspect crossings that keep the knot from coming apart. INITIALIZE

PHASE / STATUS: ACTIVE

Phase Transition Furnace

Heat and cool particles until order melts, freezes, and forms boundaries. INITIALIZE

TERRITORY / STATUS: ACTIVE

Territory Splitter

Move sites around and watch nearby space split into shifting territories. INITIALIZE

MAGNETIC / STATUS: ACTIVE

Magnetic Field Sandbox

Place poles and watch field lines and iron dust swing into alignment. INITIALIZE

SYMMETRY / STATUS: ACTIVE

Symmetry Copy Maker

Choose rotations or reflections and watch copies orbit around axes and fixed points. INITIALIZE

INTERFERENCE / STATUS: ACTIVE

Wave Interference Basin

Add wave sources and watch nodes, echoes, and interference bands spread across the basin. INITIALIZE

GRAMMAR / STATUS: ACTIVE

Rule-Grown Garden

Change rewrite rules and watch strings grow into branching plant forms. INITIALIZE

GAP / STATUS: ACTIVE

Prime Gap Constellation

Scan primes and watch long gaps, twin pairs, and density drift become a star map. INITIALIZE

MODULAR / STATUS: ACTIVE

Modular Domain Explorer

Shift, invert, and fold the upper half-plane into a domain. INITIALIZE

RADON / STATUS: ACTIVE

Projection Scanner

Scan projections, stack a sinogram, and rebuild a rough image. INITIALIZE

CRYSTAL / STATUS: ACTIVE

Crystal Growth Furnace

Seed a crystal, cool the field, and watch fronts, defects, and impurities grow. INITIALIZE

VORTEX / STATUS: ACTIVE

Vortex Flow Mixer

Add vortices, reverse spin, and watch particles twist into trails, pressure zones, and turbulent flow. INITIALIZE

NEURAL / STATUS: ACTIVE

Neural Pulse Network

Stimulate nodes, break paths, and watch pulses reroute through a changing network. INITIALIZE

IMMUNE / STATUS: ACTIVE

Virus Defense Arena

Release a virus, deploy immune cells, raise barriers, and watch spread, fatigue, and recovery fight for the field. INITIALIZE

RESISTANCE / STATUS: ACTIVE

Flow Tank Lab

Change the shape, flow, and medium, then watch dye, particles, and wake patterns gather around the body. INITIALIZE

FLOW / STATUS: ACTIVE

Obstacle Flow Lab

Place, move, and draw solid obstacles on a 2D grid, then watch the computed speed field and diagnostics respond. INITIALIZE

FLOW / STATUS: ACTIVE

Karman Vortex Tank

Run a fixed-cylinder D2Q9 LBM wake experiment and read computed speed, vorticity, density drift, and sign alternation metrics. INITIALIZE

FLOW / STATUS: ACTIVE

CFD Solver Lab

Step a browser projection-method grid solver and inspect velocity, pressure proxy, divergence, residual, boundary, and solid-mask diagnostics. INITIALIZE

CANDIDATE / STATUS: ACTIVE

AI Word Flow

Watch how a simplified AI word model passes signals across layers, then change a clue or weight and see the next-word candidates reorder. INITIALIZE

COMPLEX / STATUS: ACTIVE

Riemann Sheet Navigator

Trace a closed path through analytic branches and observe how returning to the same z can land on a different sheet. INITIALIZE

SPECTRUM / STATUS: ACTIVE

Spectral Drum

Draw a membrane, solve its six lowest vibration modes, choose a strike point, and watch shape change the spectrum and motion. INITIALIZE

TOPOLOGY / STATUS: ACTIVE

Topology Flood

Edit a point cloud, compute H0/H1 persistence, and sweep epsilon to watch components merge and one-dimensional intervals appear and disappear. INITIALIZE

OPTIMIZATION / STATUS: ACTIVE

Optimal Transport Workbench

Move supply and destination points, change their masses, and solve the globally optimal way to carry all mass at minimum total cost. INITIALIZE

MONODROMY / STATUS: ACTIVE

Polynomial Root Braid Comparator

Trace the same two coefficient loops in opposite orders and compare the computed root paths, three-dimensional braids, and final root arrangements. INITIALIZE

STRUCTURE / STATUS: ACTIVE

P-adic Lift Tree

Lift polynomial roots from mod p through powers of p, and watch each branch continue uniquely, split, die, or fail to begin. INITIALIZE

GEOMETRY / STATUS: ACTIVE

Elliptic Curve Group Law

Place two points on an elliptic curve, trace the chord or tangent, and compare exact addition over rational presets and small finite fields. INITIALIZE

STRUCTURE / STATUS: ACTIVE

Lattice Reduction Forge

Reduce a 2D integer lattice basis while keeping the lattice, determinant, and fundamental area unchanged. INITIALIZE

HYPERBOLIC / STATUS: ACTIVE

Hyperbolic Isometry Studio

Apply two disk isometries in opposite orders, then compare geodesic paths, endpoints, trace classes, and preserved hyperbolic distance. INITIALIZE

TROPICAL / STATUS: ACTIVE

Tropical Curve Balancer

Edit integer heights in a max-plus polynomial, build its tropical curve, and inspect exact vertices, weighted balancing, and the dual Newton subdivision. INITIALIZE

HODGE / STATUS: ACTIVE

Hodge Decomposition Workbench

Decompose a discrete edge field on a square-cell complex into gradient, rotational, and harmonic parts, and see how holes determine the harmonic dimension. INITIALIZE

TIME / SYNCHRONIZATION / STATUS: ACTIVE

Temporal Entrainment Chamber

Tap as one oscillator and observe phase drift, beats, phase slips, and renewed synchronization with a reference oscillator. INITIALIZE

CAUSALITY / LIGHT CONE / STATUS: ACTIVE

Causal Cone Observatory

Place events on a discrete space-time grid and watch finite local rules form future cones, causal diamonds, overlaps between future regions, and unreachable regions. INITIALIZE

TIME / SYNCHRONIZATION / STATUS: ACTIVE

Distributed Clock Network

Place local clocks on a network and observe delay, drift, offset, and temporary agreement emerge between them. INITIALIZE

TIME / ALIASING / STATUS: ACTIVE

Temporal Aliasing Observatory

Compare a continuously rotating signal with discrete samples and observe forward, frozen, or reversed readings caused by Nyquist and exposure ambiguity. INITIALIZE

TIME / SYNCHRONIZATION / STATUS: ACTIVE

Collective Synchronization Transition Field

Adjust coupling and intrinsic-frequency spread, then watch 64 autonomous oscillators move from disorder through partial synchrony toward collective order. INITIALIZE

PROBABILITY / DIFFUSION / STATUS: ACTIVE

Random Walk Diffusion Field

Release independent walkers from one origin and watch unbiased steps form a spreading cloud whose radius follows diffusion. INITIALIZE

OPTICS / DISPERSION / STATUS: ACTIVE

Prism Dispersion Observatory

Adjust incident angle, prism apex angle, and material to observe wavelength-dependent refraction, exit spectra, angular spread, and total internal reflection. INITIALIZE

LIGHT / TRANSPORT / STATUS: ACTIVE

Radiance Cascade Light Transport Field

Move one light source around fixed occluders and inspect hierarchical ray intervals, visible coverage, and sampling error in a deterministic 2D field. INITIALIZE

GEOMETRY / FRACTAL VOLUME / STATUS: ACTIVE

Sierpiński Tetrahedron Observatory

Observe a tetrahedron that keeps the same shape while its scale and volume shrink. INITIALIZE

FLOW / ADVECTION / STATUS: ACTIVE

Volumetric Advection Field

Follow a seeded density field through a velocity model and inspect advection, diffusion, flux, vorticity, and dissipation as the field moves. INITIALIZE

GEOMETRY / HARMONICS / STATUS: ACTIVE

Spherical Harmonic Surface Observatory

Adjust spherical-harmonic degree, order, amplitude, and phase to observe radial surface deformation, nodal lines, and symmetry on a sphere. INITIALIZE

WAVE / DISPERSION / STATUS: ACTIVE

Spectral Wave Surface Field

Combine spectral components on a surface and observe how wavenumber, phase, dispersion, and group velocity shape a moving wave packet. INITIALIZE

DYNAMICS / PHASE SPACE / STATUS: ACTIVE

Symplectic Map Phase-Space Observatory

Iterate an area-preserving standard map and read its phase-space trace, rotation number, finite-time Lyapunov exponent, and finite-sample regime. INITIALIZE

GEOMETRY / CURVATURE / STATUS: ACTIVE

Discrete Curvature Mesh Observatory

Read vertex angle defects, boundary geodesic curvature, Euler characteristic, and the Gauss–Bonnet residual on deterministic triangle meshes. INITIALIZE

STRUCTURE / GRAPH DIFFUSION / STATUS: ACTIVE

Graph Spectral Diffusion Field

Observe heat diffusion on a weighted graph through Laplacian eigenmodes, spectral gap, heat trace, and community mixing. INITIALIZE

STRUCTURE / DENSITY GEODESIC / STATUS: ACTIVE

Optimal Transport Density Geodesic Observatory

Observe a balanced one-dimensional density transport plan through monotone coupling, displacement geodesics, W2 cost, entropy, and barycenters. INITIALIZE

STRUCTURE / DIFFRACTION / STATUS: ACTIVE

Quasicrystal Diffraction Observatory

Observe an Ammann–Beenker quasicrystal from a 4D cut-and-project window: accepted points, local coordination, eightfold rotation, and S(k) diffraction peaks. INITIALIZE

SCALE / RENORMALIZATION GROUP / STATUS: ACTIVE

Renormalization Flow Observatory

Block-spin coarse-grain a 2D Ising-like lattice and observe magnetization, correlations, and effective-coupling flow across scale. INITIALIZE

FIELD / EIKONAL WAVEFRONT / STATUS: ACTIVE

Eikonal Geodesic Wavefront Observatory

Observe arrival time, wavefronts, and fastest paths in a positive speed field with a deterministic eight-neighbour eikonal graph. INITIALIZE

QUANTUM / HOLONOMY / STATUS: ACTIVE

Berry Phase Holonomy Observatory

Carry a two-level eigenstate around closed loops on the Bloch sphere and compare its Berry phase with the enclosed curvature. INITIALIZE

CRITICAL POINT / LEVEL SET / STATUS: ACTIVE

Morse Landscape Observatory

Read critical points and sublevel-set changes in a finite two-dimensional scalar landscape. INITIALIZE

CATASTROPHE / EQUILIBRIA / STATUS: ACTIVE

Catastrophe Surface Observatory

Follow real equilibrium branches as folds, cusps, and hysteresis emerge from a quartic potential. INITIALIZE

NOETHER / CONSERVATION / STATUS: ACTIVE

Noether Symmetry Conservation Observatory

Observe how translation, rotation, and time symmetry carry a charge, and how an explicit breaking term makes its balance drift. INITIALIZE

MODULAR / FAREY TESSELLATION / STATUS: ACTIVE

Modular Geodesic Tessellation Observatory

Read PSL(2,Z) reduction, Ford circles, Farey adjacency, and continued-fraction itineraries as one exact upper half-plane observation. INITIALIZE

WAVE / NONLINEAR DISPERSION / STATUS: ACTIVE

Soliton Scattering Field

Observe exact KdV single and two-soliton profiles: amplitude-speed coupling, collision phase shifts, conserved integrals, and a finite-difference PDE residual. INITIALIZE

STRUCTURE / RANDOM GRAPH / STATUS: ACTIVE

Random Graph Giant Component Observatory

Observe the emergence of a giant connected component in an Erdős–Rényi random graph as the mean degree c crosses the finite-size threshold near 1. INITIALIZE

DEFECT / WINDING / STATUS: ACTIVE

Topological Defect Winding Observatory

Observe vortices, anti-vortices, winding, current, and energy in a 64×64 periodic XY phase field. INITIALIZE

STRUCTURE / CATENARY EQUILIBRIUM / STATUS: ACTIVE

Catenary Chain Observatory

Observe the static catenary of a uniform flexible chain and read how span, chain length, linear density, and gravity set its sag and support tension. INITIALIZE

STRUCTURE / CAPILLARY BALANCE / STATUS: ACTIVE

Capillary Rise Observatory

Observe Jurin-law capillary rise or depression as surface tension balances hydrostatic pressure in a deterministic tube model. INITIALIZE

PARTICLE / TRACK VISIBILITY / STATUS: ACTIVE

Cloud Chamber Track Observatory

Observe a seeded ensemble of charged-particle candidates and how supersaturation and cooling select a visible track fraction. INITIALIZE

FIELD / PHOTOELASTIC STRESS / STATUS: ACTIVE

Photoelastic Stress Observatory

Observe a deterministic 2D photoelastic surrogate: load a sample, rotate the polarizers, and read relative principal-stress difference patterns. INITIALIZE

DYNAMICS / POINCARé SECTION / STATUS: ACTIVE

Double Pendulum Poincaré Observatory

Observe a continuous-time double pendulum through a deterministic Poincaré section and compare regular-island and chaotic-sea candidates without claiming a formal chaos proof. INITIALIZE

QUANTUM / TUNNELING / STATUS: ACTIVE

Quantum Tunneling Observatory

Change a finite barrier and observe the connected quantum wave, transmitted flux, and reflected flux in stationary scattering. INITIALIZE

GEOMETRY / MINIMAL SURFACE / STATUS: ACTIVE

Catenoid Minimal Surface Observatory

Separate two coaxial rings and observe two catenoid branches, their areas, curvatures, and the limit of a connected minimal surface. INITIALIZE

LATTICE / BAND GAP / STATUS: ACTIVE

Phononic Band Gap Observatory

Change alternating masses to open a frequency gap. Select a Bloch wave and observe its acoustic or optical motion in a periodic chain. INITIALIZE

OPTICS / DIFFRACTION / STATUS: ACTIVE

Fresnel Diffraction Observatory

Change a slit, wavelength, and screen distance. Observe near-field fringes becoming a far-field diffraction pattern. INITIALIZE

DYNAMICS / BILLIARD / STATUS: ACTIVE

Dynamical Billiard Observatory

Change the boundary and follow a point through free flight and mirror-like collisions. Compare its path with the same collisions on a boundary map. INITIALIZE

STOCHASTIC / ESCAPE / STATUS: ACTIVE

Kramers Escape Observatory

Watch thermal fluctuations carry independent paths to a barrier top. Compare survival, first-arrival times, and a continuum reference. INITIALIZE