Wave 17 pressed into some of the most technically demanding territory we’ve covered to date: the Riemann hypothesis and post-quantum lattice cryptography, renormalization group fixed points and universality classes, and the Hodgkin-Huxley equations that describe how every action potential in every brain on earth is generated. On the infrastructure side, this wave brought a complete rebuild of the platform search system — replacing keyword substring matching with an inverted-index model, adding tag faceting, and introducing a three-tier difficulty classification across all 345 simulations.
Platform Stats
Wave 17 Content
Spotlight #34 – Number Theory & Cryptography
From the prime number theorem and Riemann’s zeta function through RSA key mechanics, elliptic curve group law, NIST PQC finalists (CRYSTALS-Kyber/Dilithium), and interactive Schnorr zero-knowledge proofs — the mathematical foundations that secure every TLS connection. ~13 min.
Learning #27 – Statistical Mechanics & Phase Transitions
Partition functions and Boltzmann statistics, the exact 2D Ising solution (Onsager 1944, critical exponents β = 1/8), Landau order-parameter theory, Wilson’s renormalization group and universality, the fluctuation-dissipation theorem, and Metropolis & Wolff Monte Carlo near the critical point. ~14 min.
Spotlight #35 – Neuroscience & Neural Circuits
Hodgkin-Huxley conductance equations and action potential generation, quantal synaptic transmission and short-term plasticity, Hebbian learning and spike-timing-dependent plasticity, Wilson-Cowan neural mass oscillations, connectome graph theory, and The Virtual Brain whole-brain simulation framework. ~13 min.
Search 2.0: Inverted Index Architecture
The original search system performed a linear scan across all simulation titles and descriptions on each keystroke, which worked adequately at 50 simulations but became noticeably slow at 345. More importantly, it could not rank results by relevance, support multi-term queries correctly, or filter by structured metadata. Search 2.0 addresses all of these limitations.
Inverted Index
At build time, all simulation metadata is tokenised: titles,
descriptions, category names, and tags are split on whitespace and
punctuation, lowercased, and written into a
searchIndex.json where each token maps to a posting list of
simulation IDs. At query time, the user’s input is tokenised
identically; for each query token, the corresponding posting list is
retrieved and the intersection (AND) or union (OR) of IDs is computed in
O(k log n) time where k is the posting list length.
Full-Text Search
All 345 simulation titles, descriptions, tags, and category names indexed into a token → ID inverted index. Sub-10 ms query latency at full scale.
Tag Faceting
Tag chips rendered as toggle filters that narrow the result set by intersection. Multi-select facets allow pendulum AND chaos combinations.
Relevance Ranking
TF-IDF-inspired scoring: title matches weighted 3×, description 1×. Results sorted descending by score; ties broken by simulation date.
Instant Results
Results update on every keystroke with 16 ms debounce. Zero network requests: the entire index is loaded once as a static JSON file.
Schema Changes
Each simulation record in simulations.json now carries two
new fields:
-
"difficulty": "beginner" | "intermediate" | "advanced"— manually curated, reviewed for all 345 simulations -
"tags": ["string", ...]— controlled vocabulary, 3–8 per simulation, drawn from a 120-term taxonomy
The difficulty field drives a three-tier badge system visible on simulation cards and in search results. The tag field populates the facet side-bar and improves full-text recall for domain-specific queries.
Simulation Difficulty Classification
No prerequisites beyond secondary school physics or mathematics. Interactive controls encourage exploration. ~40% of simulations.
Familiarity with calculus, basic mechanics or introductory programming helpful. Parameters have physical significance. ~45% of simulations.
University-level mathematics or physics assumed. Models involve PDEs, statistical mechanics or quantum formalism. ~15% of simulations.
Learning Paths
One of the most requested features has been curated sequences of simulations that build conceptual understanding progressively. Six initial learning paths are now live:
- Classical Mechanics (12 sims) — projectile → pendulum → orbital → chaos
- Waves & Optics (10 sims) — standing waves → diffraction → laser labyrinth → holography
- Electromagnetism (9 sims) — static electricity → field lines → LC circuit → Maxwell equations
- Thermodynamics (11 sims) — ideal gas → Carnot → Ising model → Maxwell-Boltzmann → phase transitions
- Quantum Mechanics (8 sims) — double-slit → tunneling → hydrogen atom → BB84
- Data Science (9 sims) — linear regression → k-means → neural network → decision tree
Each path page displays a horizontal stepper showing the user’s
progress (stored in
localStorage), links to each simulation, and a brief
rationale for why that step follows from the previous one. Paths are
defined in a new shared/data/learning-paths.json file and
rendered client-side.
Search Performance Audit
- ✓ Query latency: median 4 ms, 99th percentile 11 ms (Chrome DevTools Performance, corpus of 345 sims)
- ✓ Index size: 28 KB (gzip), loaded once on first search interaction
- ✓ Full-text recall: all 35 manually constructed test queries return expected top result in position 1
- ✓ Tag facets: intersection logic verified for all 120 tags × 345 simulations
- ✓ Difficulty badges: all 345 simulations classified; classification reviewed by 3 contributors
- ✓ Learning paths: all 6 paths tested end-to-end; localStorage progress persists across sessions
- ✓ Keyboard navigation: search field, facet chips, and result cards all keyboard-accessible
- ⚠ Fuzzy matching (edit distance ≤ 1) deferred to Wave 18 — typo tolerance not yet implemented
Wave 18 Preview
Plasma Physics & Fusion
Tokamak confinement, Lawson criterion, MHD stability, ITER engineering and the physics of Z-pinch and inertial confinement fusion.
Topology & Manifolds
Surfaces, genus, Euler characteristic, fundamental groups, covering spaces, fibre bundles, and the classification of compact surfaces.
Materials Science & Dislocations
Crystal defects, Burgers vector, dislocation motion and strain hardening, phase diagrams, and semiconductor band engineering.
Fuzzy Search & Mobile UX
Edit-distance fuzzy matching, phonetic name matching, improved touch controls across all simulations, and PWA offline reliability improvements.