Sound & Music (7)
Musical Scales sound
Compares just intonation, Pythagorean, and 12-tone equal temperament, where each semitone is the frequency ratio 2^(1/12) ≈ 1.0595, so twelve steps double the pitch to an octave.
Acoustic Guitar String sound
A plucked string vibrates as a sum of standing-wave harmonics with f_n = (n/2L)√(T/μ), so tension, length, and linear density set the fundamental and the timbre comes from the harmonic mix.
Beat Frequency sound
Two close tones superpose into an amplitude envelope that throbs at the difference frequency f_beat = |f₁ − f₂|, the effect piano tuners listen for.
Echolocation sound
A bat emits a chirp and times the echo to range a target via d = c·t/2, while the Doppler shift of the return reveals the prey's closing velocity.
Voice Synthesis sound
A source-filter model passes a glottal pulse train through resonant formant filters, whose peak frequencies (F1, F2) shape the vowel you hear.
Acoustic Impedance sound
At a boundary between two media the pressure reflection coefficient R = (Z₂ − Z₁)/(Z₂ + Z₁) with Z = ρc explains why ultrasound needs gel and why air–tissue interfaces echo strongly.
Active Noise Cancellation sound
An anti-phase wave (180° shifted) is summed with incoming noise so destructive interference drives the residual toward zero, the principle behind ANC headphones, tuned by an adaptive LMS filter.
Geology & Environment (11)
Landslide Stability geology
An infinite-slope model computes the factor of safety FS = (c + (σ − u)tanφ) / τ; once pore-water pressure pushes FS below 1, the slope fails.
Permafrost Thaw geology
Heat diffusion through frozen ground (Stefan problem) advances the active-layer depth as √t while latent heat of fusion buffers the melt front against rising air temperature.
Forest Succession geology
A Markov transition model steps bare ground → grasses → shrubs → pioneer trees → climax forest, with disturbance probabilities resetting patches to earlier seral stages.
Ocean Current geology
The Coriolis force deflects wind-driven flow into an Ekman spiral and western-boundary intensification, producing gyres and the surface transport that redistributes planetary heat.
Arctic Sea Ice geology
The ice-albedo feedback loop: as ice (albedo ≈ 0.6) melts to open ocean (albedo ≈ 0.06), more absorbed sunlight accelerates further melt, a positive feedback that can tip rapidly.
Wind Erosion geology
Once wind shear exceeds the threshold friction velocity, saltating grains bombard the surface and dunes migrate downwind, with flux scaling as roughly u*³.
Urban Heat Island geology
A surface energy balance shows how low-albedo asphalt, reduced evapotranspiration, and anthropogenic heat raise city temperatures several degrees above the surrounding countryside, mitigated by green roofs and trees.
Sandstone Formation geology
Burial compaction and cementation reduce porosity over time, φ = φ₀·e^(−c·z), as quartz and carbonate precipitate in the pore space to lithify loose sand into rock.
Climate Tipping Points geology
A double-well potential with a saddle-node bifurcation shows how a slowly forced climate system can cross a threshold into an abrupt, hysteretic regime shift that resists reversal.
Earthquake Fault geology
A spring-block stick-slip model loads elastic strain until static friction is overcome, releasing energy in events whose magnitudes follow the Gutenberg-Richter power law.
Soil Profile geology
Weathering and leaching build the O-A-B-C horizons over time as organic matter, clay illuviation, and parent-material breakdown stratify the soil column.
Physics & Computing (10)
Plasma Wave physics
Electron density oscillates at the Langmuir plasma frequency ω_p = √(n e² / ε₀ m_e), the natural ringing that sets a plasma's optical cutoff and Landau damping.
Electromagnetic Wave physics
Maxwell's equations yield self-propagating, mutually perpendicular E and B fields travelling at c = 1/√(μ₀ε₀), with polarization and Poynting energy flux shown in 3D.
Fluid Instability physics
Kelvin-Helmholtz and Rayleigh-Taylor instabilities roll up shear layers and density inversions into billows and mushroom plumes once the growth rate exceeds stabilising surface tension.
Reed-Muller Code computing
The RM(r,m) error-correcting code encodes via Boolean monomials and decodes by majority-logic voting, the family famously flown on Mariner 9 for Mars imagery.
CRC Checksum computing
Cyclic redundancy check treats the message as a polynomial over GF(2) and appends the remainder of division by a generator polynomial, catching burst errors in Ethernet and ZIP files.
LZ77 Compression computing
A sliding window replaces repeated substrings with (offset, length, next-char) back-references, the dictionary core inside DEFLATE, gzip, and PNG.
Quantum Error Correction computing
The surface code spreads one logical qubit across a lattice of physical qubits, using stabiliser syndrome measurements to detect and correct bit- and phase-flips below threshold.
Crystal Dissolution physics
A kinetic Monte Carlo model removes atoms preferentially from high-energy kink and step sites, so dissolution rate tracks undersaturation and the etched morphology reveals crystal symmetry.
Fractal Landscape physics
The diamond-square algorithm builds self-similar terrain from fractional Brownian motion, where the Hurst exponent H tunes ruggedness from rolling hills to jagged peaks.
Origami Fold physics
A rigid-origami crease pattern must satisfy Maekawa's theorem (mountains minus valleys = ±2) and Kawasaki's alternating-angle condition to fold flat without tearing.
Space (2)
Pulsar space
A rotating neutron star sweeps a magnetic-dipole beam past Earth like a lighthouse, its spin period lengthening as magnetic braking radiates rotational energy.
Black Hole Thermodynamics space
Hawking temperature T = ℏc³/(8πGMk_B) means smaller black holes are hotter, evaporating faster as their Bekenstein-Hawking entropy (proportional to horizon area) is radiated away.
Biology, Genetics & Machine Learning (10)
Bioluminescence biology
The luciferin-luciferase reaction oxidises luciferin to emit a photon, a near-100%-efficient cold light whose colour depends on the enzyme variant.
Coevolution biology
Predator and prey traits chase each other in a Red Queen dynamic, where reciprocal selection keeps both species evolving just to maintain relative fitness.
Bacteria Competition biology
Lotka-Volterra competition for a shared nutrient drives the species with the lower R* (break-even resource level) to competitive exclusion of its rival.
Epigenetics genetics
DNA methylation and histone modification act as a bistable switch that silences or activates genes heritably without changing the underlying sequence.
Biofilm Formation biology
Cells attach, secrete an EPS matrix, and grow via Monod kinetics μ = μ_max·S/(K_s + S), with quorum sensing triggering the mature, antibiotic-tolerant community.
Cell Signaling Cascade biology
A MAPK kinase cascade converts a graded ligand input into a switch-like, ultrasensitive response via Goldbeter-Koshland zero-order amplification at each tier.
Magnetic Navigation biology
Migratory animals read the geomagnetic inclination angle (and possibly a radical-pair quantum compass) to orient, mapping field-line dip to latitude.
Predator-Prey Evolution biology
An eco-evolutionary model couples Lotka-Volterra population cycles to heritable speed traits, so selection pressure and abundance oscillate together.
Self-Organizing Map ai-ml
Kohonen's SOM trains a 2D neuron grid so that nearby neurons respond to similar inputs, producing a topology-preserving low-dimensional map of high-dimensional data.
RBF Network ai-ml
A radial basis function network sums Gaussian kernels φ(r) = exp(−r²/2σ²) centred on prototypes, fitting smooth nonlinear surfaces with a single linear output layer.
Energy & Engineering (3)
Heat Pipe engineering
A sealed two-phase device moves heat by evaporating working fluid at the hot end and condensing it at the cold end, with capillary wick return giving an effective conductivity far above solid copper.
Wave Energy Converter engineering
An oscillating water column drives air through a Wells turbine; captured power scales with the wave-energy flux P = (ρg²/64π)·H²T per metre of crest.
Desalination engineering
Reverse osmosis forces seawater through a membrane above its osmotic pressure (Π ≈ iMRT ≈ 27 bar for seawater), leaving salts behind to yield fresh water.
Palaeoclimate & Dating (5)
Ice Core Record palaeo
Trapped air bubbles and the δ¹⁸O ratio in layered ice reconstruct past CO₂ concentration and temperature back hundreds of thousands of years.
Dendrochronology palaeo
Cross-dating overlapping tree-ring width patterns builds a continuous chronology, since wide rings mark favourable years and narrow rings mark drought or cold.
Pollen Analysis palaeo
Pollen grains preserved in lake sediment record shifting vegetation assemblages, letting a palynologist reconstruct past climate from the relative tree-vs-grass abundance down-core.
Isotope Dating palaeo
Radioactive decay N = N₀·e^(−λt) turns the parent-to-daughter ratio into an absolute age clock, from radiocarbon (t½ = 5730 yr) to uranium-lead for deep time.
Reef Bleaching palaeo
Accumulated thermal stress measured in degree-heating-weeks expels the symbiotic zooxanthellae, bleaching the coral and recording ocean-warming events in the reef's growth bands.
Category Coverage Improvements
Wave 103 was the broadest single push in the project's history. The headline change is a brand-new palaeoclimate and proxy-dating column, plus the deepest single-wave growth the acoustics and geology categories have ever seen.
Physics Covered: A Closer Look at Four Sims
Equal Temperament — The Geometry of Musical Scales
Why does a piano sound in tune in every key? Because 12-tone equal temperament divides the octave into twelve geometrically equal steps. Each semitone multiplies the frequency by the twelfth root of two, so stacking twelve of them lands exactly on the octave (a factor of two). This sacrifices the pure integer ratios of just intonation — the equal-tempered fifth is a couple of cents flat — in exchange for being able to modulate freely between keys.
Equal temperament: f_n = f_0 * 2^(n/12)
n : semitones above reference
A4 reference: 440 Hz
Semitone ratio: 2^(1/12) = 1.059463...
Just fifth (3:2) = 701.96 cents ; ET fifth = 700 cents (-1.96)
Cents between two frequencies: 1200 * log2(f2 / f1)Permafrost Thaw — The Stefan Moving-Boundary Problem
When the surface warms, a thaw front advances downward into frozen ground. This is a classic Stefan problem: heat conducts ahead of the front, but at the front itself energy is consumed melting pore ice (latent heat of fusion). Because that latent-heat sink must be overcome before the boundary can move, the thaw depth grows with the square root of time rather than linearly — the same diffusive scaling seen across heat and mass transport.
Thaw depth: X(t) = lambda * sqrt(t)
Stefan condition at the front:
k * dT/dx = rho * L_f * dX/dt
L_f : latent heat of fusion of ice (334 kJ/kg)
k : thermal conductivity of thawed soil
Active-layer depth tracks surface degree-days above 0 C.LZ77 — Compression by Back-Reference
LZ77 is the dictionary half of nearly every general-purpose compressor in use today. It slides a window over the data; whenever the upcoming bytes match a sequence already seen inside the window, it emits a compact (offset, length) pointer back into that history instead of the literal bytes. The longer and more frequent the repeats, the better the ratio. DEFLATE (gzip, PNG, ZIP) pairs this with Huffman coding of the resulting tokens.
Token: (offset, length, next_literal)
offset : distance back into the sliding window
length : number of matched bytes to copy
Encode "abcabcabcx":
a -> (0,0,a)
b -> (0,0,b)
c -> (0,0,c)
abcabc -> (3,6,x) // copy from 3 back, 6 bytes, then 'x'
Decompression copies byte-by-byte, allowing overlap.Surface-Code Quantum Error Correction
Physical qubits decohere far too fast to run long quantum algorithms directly. The surface code protects a single logical qubit by entangling it across a 2D lattice of physical qubits and repeatedly measuring local stabiliser operators. Those measurements never reveal the encoded data, but their parity (the syndrome) flags where bit-flip or phase-flip errors occurred, and a matching decoder corrects them — provided the physical error rate stays below the code threshold (around 1%).
Distance-d surface code: d^2 data qubits + (d^2 - 1) measure qubits
Logical error rate falls exponentially in d below threshold:
P_L ~ (p / p_th)^(d/2)
p : physical error rate per gate
p_th : threshold (~0.01 for the surface code)
Z-stabilisers catch X (bit-flip) errors; X-stabilisers catch Z (phase) errors.
Decoder: minimum-weight perfect matching on the syndrome graph.Infrastructure Updates
Sitemap and feed scale
Adding 47 simulations in one wave — each with English, Ukrainian, and Polish landing pages — expanded the sitemap by well over a hundred URLs. The generator now batches sitemap writes and re-pings the search consoles only once per deploy rather than per page, cutting build time noticeably on the larger wave.
Accessibility audit
All 47 Wave 103 simulations passed an automated axe-core audit before merge. The acoustics sims got extra attention: every audio-producing simulation now requires an explicit user gesture before sound plays, exposes a visible mute control, and announces playback state via an aria-live region for screen-reader users.
Performance budgets
The per-frame performance budget introduced in Wave 98 caught two regressions this wave — the fractal-landscape diamond-square mesh and the plasma-wave particle field both exceeded the 16 ms budget on throttled mobile. Both were fixed by capping resolution on small viewports and reusing typed-array buffers between frames.
Up Next
Wave 104 will deepen the new palaeoclimate column with sediment-varve counting and a foraminifera assemblage proxy, and revisit acoustics with room reverberation (image-source method) and a vocoder. We are also scoping a second machine-learning batch around attention mechanisms and graph neural networks. Browse all posts in the blog archive or jump to the companion spotlights for a deeper look at the physics behind these simulations.