Playground ·
A generative melody box
A WebAudio toy that improvises a melody with a random walk over a pentatonic scale, plus a drone and an echo — silent until you press Play.
Learning
Subjects I am studying and the books and notes that came out of them.
Biology and medicine 32Mathematics 58Chemistry 10Physics 39
Playground ·
A harmonograph drawing machine
Four decaying pendulums steer a pen; frequencies near simple ratios draw the spirograph-like curves Victorian harmonographs were famous for.
Playground ·
A raymarched scene
A whole 3-D scene — a blobby shape on a checkered floor, soft shadows, an orbiting camera — drawn by one fragment shader with no triangles at all.
Playground ·
BQN playground
BQN, a modern APL, in your browser — whole-array primitives, folds and scans, tables, and tacit trains like (+´÷≠) for the mean.
Playground ·
Boids
Craig Reynolds' flocking model — three local rules per bird, and a flock emerges; the mouse is a predator.
Playground ·
FizzBuzz in nineteen languages
The smallest interesting program, written the way each language would write it — from JavaScript and Rust to SQL, Prolog, BQN, Forth and a Befunge maze. Every block runs and prints the same twenty lines.
Playground ·
Flow fields
Thousands of particles drifting through a Perlin-noise vector field, leaving trails that pile up into silk.
Playground ·
Fortran playground
Modern Fortran compiled in your browser by LFortran — whole-array arithmetic, matrix intrinsics, modules and derived types, and a numerical kernel solving the heat equation.
Exploration ·
How a brushless motor spins
From magnets and coils to a quadcopter in the air: how a brushless motor is wound, how an ESC switches it in six steps, how it finds the rotor without sensors, what field-oriented control does better, and what happens when you bolt four of them to a frame — with the simulators running alongside.
Exploration ·
How a jet engine makes thrust
Follow a parcel of air through a jet engine — squeezed, burned, expanded, thrown out of the back — with the cycle worked out live at every step, then see why airliner fans keep growing and why a car's turbocharger is a little gas turbine.
Tool ·
Jet engines and gas turbines
How jet engines work and what their numbers mean: an animated cutaway of turbojet, turbofan, turboprop, turboshaft, ramjet and afterburning engines with numbered stations; ideal and real Brayton cycle analysis at any Mach and altitude — thrust, TSFC, efficiencies, T–s and P–v diagrams and trade studies; compressor stages, draggable velocity triangles and a compressor map with surge margin; approximate figures for real engine families; and fuel, run time and start-up for model turbojets.
Playground ·
L-system plants
A few rewriting rules and a turtle grow a meadow of plants that are never quite the same twice.
Playground ·
Life with colour trails
Conway's Game of Life where live cells are coloured by age and dead ones leave a fading ghost, so you can see where the action has been.
Playground ·
N-body: a small solar system, timed
The same five-body gravity simulation in fifteen languages, each timing itself — a hands-on look at how much the runtime matters when the program is all floating-point arithmetic in a tight loop.
Playground ·
R playground
Real R running in your browser through webR — vectors, data frames, a linear model with its summary, simulation, and base-graphics plots.
Playground ·
Reaction–diffusion
The Gray–Scott model — two imaginary chemicals that spread and react — grows coral, fingerprints and dividing cells from a few drops.
Playground ·
The Mandelbrot set as ASCII art
Nested loops and floating-point arithmetic in eighteen languages — plain loops, complex numbers, whole-array versions in R and BQN, and a recursive query in SQL — all drawing the same 66 × 23 picture, character for character.
Exploration ·
Why sourdough rises
A jar of flour and water raises a loaf with no packet of yeast. Follow it from the microbes in the starter, through temperature, time, water and gluten, to the oven — with the sourdough, bread and artisan-bread tools open beside the text.
Tool ·
Marble tilt
Roll a steel marble through a maze on a tilting 3D board — holes, railed and narrow bridges, moving platforms, bumpers and checkpoints — by tilting your phone, dragging, or with keys or a gamepad. Twelve designed levels, endless levels from a seed, and best times.
Tool ·
Mine Sphere
Minesweeper on a globe of hexagons and twelve pentagons — five sizes, three densities, chording, a first click that is always safe, and an optional no-guess board that a built-in solver proves can be cleared by logic.
Tool ·
Control systems
Enter a plant as a transfer function — polynomials or poles, zeros and gain, continuous or sampled — or pick a DC motor, mass–spring–damper, inverted pendulum, thermal or dead-time preset, add a P, PI, PID or lead/lag controller, and see the step and impulse responses with rise, overshoot, settling and steady-state error, the Bode plot with gain and phase margins, the Nyquist plot, a root locus you drag the gain along, and the closed-loop pole–zero map, with Ziegler–Nichols, IMC and SIMC tuning.
Tool ·
Earthquakes, live
Earthquakes from the USGS live feeds (past hour to past 30 days) or any date range from its catalogue, on a world map with plate boundaries — sized by magnitude, coloured by depth or age — with a filterable list, details (PAGER alert, felt reports, tsunami flag, ShakeMap), distance from you and when the P and S waves reach you, a Gutenberg–Richter plot with the b-value, and what each step of magnitude means in energy.
Tool ·
Eclipses and meteor showers
Every solar and lunar eclipse from 2020 to 2050 with its times and how much you'll see from your place — contacts, magnitude, obscuration, the path of totality on a world map — and the meteor showers of the IMO list, with the rate you can expect tonight after the radiant's height, your sky and the moon.
Tool ·
Kalman filter playground
Tune a Kalman filter live and watch it work — a 1-D value, 2-D tracking with constant-velocity and constant-acceleration models, an extended Kalman filter for a range–bearing sensor, GPS + accelerometer fusion, and complementary filter against Kalman for tilt (with your phone's sensors) — stepping through predict and update with every matrix shown, covariance ellipses, innovations and NIS/NEES consistency against chi-square bounds.
Tool ·
Observing planner
What's worth looking at tonight: the Messier and Caldwell objects and some showpiece stars ranked for your place, sky and telescope through the dark hours, each with an altitude chart; the night's cloud, transparency and dew forecast; a saved observing list, a session log you can download, and the Messier marathon's best night and running order.
Tool ·
Phone seismograph
Your phone's accelerometer as a seismograph: a live three-axis trace with gravity and tilt filtered out, a helicorder (drum) view, an STA/LTA trigger with an event log, peak ground acceleration in g with the approximate Modified Mercalli intensity, a spectrum to see what is shaking (footsteps, a washing machine), and recordings saved as CSV or WAV. A demo mode makes synthetic earthquakes on a desktop.
Tool ·
Piano and guitar trainer
Learn songs on the piano or guitar: notes fall onto a keyboard with finger numbers and the staff scrolls along, or the song appears as tab, on a fretboard and as chord charts with a strumming pattern. Watch it, let it wait for you, or play along and get scored — with a MIDI keyboard, the computer keys, touch, or the microphone — and import your own MIDI and MusicXML files.
Tool ·
Planet details
The planets in your eyepiece, drawn to scale at your magnification and flipped the way your telescope shows them: Jupiter's four big moons and their transits, shadows, eclipses and occultations, and when the Great Red Spot crosses; Saturn's ring tilt and its moons; Mars's central meridian and markings; Venus's and Mercury's phases.
Tool ·
Planet events and alignments
Conjunctions of planets with each other, the Moon and bright stars, planet "parades", oppositions, greatest elongations, stations and retrograde loops, Mars's closest approach and lunar occultations — for the next year or twenty, filtered to what you can actually see from your place, each with a picture of the sky at the best moment and an .ics file for your calendar.
Tool ·
Reinforcement learning gridworld
A gridworld you paint — walls, pits, goals, wind and slippery ice — solved by value iteration and policy iteration, and learned by Q-learning, SARSA and Expected SARSA with ε-greedy exploration; value heatmap, policy arrows, Q-values per cell, the reward curve, the cliff-walking race between Q-learning and SARSA, and every Bellman backup written out with the live numbers.
Tool ·
Skew-T sounding
A Skew-T log-P diagram for any place from Open-Meteo's forecast, or for a radiosonde sounding pasted from the University of Wyoming — temperature and dewpoint, dry and moist adiabats, mixing-ratio lines, wind barbs, a surface, mixed-layer or most-unstable parcel with CAPE and CIN shaded, LCL, LFC and EL, lifted index, precipitable water, freezing level, shear, storm motion and helicity, a hodograph, and a plain-English reading.
Tool ·
Sky darkness
Convert between the Bortle class, sky brightness in mag/arcsec² (an SQM reading), naked-eye limiting magnitude and how much brighter than natural your sky is; see what each class shows and a simulated star field at that darkness; and estimate tonight's limiting magnitude by altitude with the Moon up.
Tool ·
Sky tonight
A star chart for your place and time — the whole sky as a dome or a zoomable view, with stars to magnitude 6.5, constellations, the Milky Way, Messier objects, the planets and the Moon's phase; a time slider, search, rise/transit/set for anything you tap, a red night mode, and a mode that shows what your phone is pointing at.
Tool ·
Telescope mount
Polar alignment (where Polaris or σ Octantis sits on your polar-scope reticle right now, and drift alignment), setting circles (RA/Dec to altitude and azimuth and back, hour angle, sidereal time), and a GoTo controller over Web Serial for Celestron NexStar, Sky-Watcher SynScan and Meade LX200 mounts — connect, read where it points, slew, sync, nudge and stop. It refuses to slew near the Sun.
Tool ·
Train a tiny transformer
Train a character-level, decoder-only transformer from scratch in your browser — one to four layers, written in plain JavaScript with a hand-written backward pass checked against finite differences — on Shakespeare's sonnets, nursery rhymes, Carroll and Lear, or your own text, and watch the loss fall, the samples turn into words, the attention heads specialise and the character embeddings sort themselves out.
Tool ·
Z3 solver playground
Microsoft Research's Z3 SMT solver running in the page — an SMT-LIB editor with readable models, puzzles that show the SMT-LIB they generate (Sudoku, N-queens, SEND+MORE=MONEY, magic squares, job scheduling, exam timetabling), and a small C-like language for proving bit tricks and finding overflow bugs.
Tool ·
Heat loss and HVAC sizing
A room-by-room heat-loss and cooling-load estimate in the style of Manual J (not Manual J): U- or R-values and areas, air leakage, design temperatures for a few US cities with sources, window solar gain from the sun's position, and heat-pump sizing with the balance point — in imperial or metric.
Tool ·
Maths practice gym
Practise the skills from arithmetic to intro calculus — a skill tree of 33 skills, generated problems checked by equivalence, step-by-step checking that names your mistakes, timed drills, an adaptive placement test, and spaced-repetition review, with progress kept in your browser.
Tool ·
Ocean lab
Predict tides from NOAA harmonic constituents and check them against NOAA's own predictions; solve the wave dispersion relation, grow wind waves, shoal and break them; compute TEOS-10 seawater properties with a T–S diagram and CTD profiles; work out Coriolis, Ekman and geostrophic currents; and plot NDBC buoy observations.
Tool ·
Spaced-repetition flashcards
Flashcards for Mathematics, Reconnected, Human Biology for the Medical Maker and the AI Acceleration primer — definitions, formulas, mastery checks and glossaries, each linked to its chapter — plus Big-O and coding interview decks that go with this site's tools — scheduled with FSRS (or SM-2), with cloze cards, your own decks, CSV and Anki import and export, and statistics, kept in your browser.
Tool ·
Beams, columns and trusses
Beam solver for simply supported, cantilever, propped, fixed and overhanging beams with point, uniform, triangular and moment loads — shear, moment, slope and deflection diagrams, stresses from a section-property calculator, steel, aluminium, wood and 3D-printed materials — plus Euler and Johnson column buckling and a drawable 2-D truss solver with tension, compression and member buckling.
Tool ·
Classic machine learning, step by step
Classic machine learning on 2-D data you can edit — a decision tree growing split by split with its best-split search, a random forest's bootstrap trees and vote map, gradient boosting round by round, k-NN, logistic regression, a soft-margin linear SVM and Gaussian naive Bayes side by side — and an optimiser lab racing SGD, momentum, Nesterov, AdaGrad, RMSProp, Adam and AdamW over Rosenbrock, Beale, a saddle and an ill-conditioned bowl with learning-rate schedules.
Tool ·
Digital logic simulator
Build digital circuits by dragging gates, switches, clocks, LEDs and 7-segment displays, watch the signals light up, and go further with flip-flops, counters, adders, an ALU, RAM and ROM, your own sub-circuits, truth tables with minimised expressions, expression-to-circuit, a timing diagram with real gate delays, and a tiny CPU that runs a program.
Tool ·
Embedding explorer
Load embeddings (CSV, TSV, JSON, GloVe text, the TensorFlow Projector's vectors.tsv + metadata.tsv) or embed sentences in the browser with all-MiniLM-L6-v2, then project them with PCA, t-SNE or UMAP in 2-D or 3-D, colour and search them, list nearest neighbours by cosine or Euclidean distance, cluster with k-means or DBSCAN, score how faithful the map is, and try word analogies.
Tool ·
HDL trainer: learn Verilog by doing
Learn Verilog by writing it: 23 lessons from gates to UARTs, VGA timing, FIFOs and pipelines, each checked by a hidden testbench that simulates your module and shows the waveform and every mismatch — plus a sandbox simulator and a logic-sim → Verilog converter.
Tool ·
Lasers and fibre optics
Gaussian beams (waist, Rayleigh range, divergence, w(z), R(z), Gouy phase, M²), focusing to a spot and beam expanders, ABCD q-parameter propagation through a train of lenses with an animated full-screen envelope plot, two-mirror cavity stability on the g₁g₂ diagram, fibre NA, V number, modes, cutoff and Marcuse mode field diameter, a dB link budget, modal and chromatic dispersion, approximate laser-safety MPE and NOHD, and photon arithmetic.
Tool ·
Lens design bench
A sequential lens design bench: build a prescription of spherical and conic surfaces in N-BK7, N-SF11, F2, N-SK16, fused silica, CaF₂ and plastics (Sellmeier data), trace paraxial and real rays, get the cardinal points, Seidel aberrations and longitudinal colour, spot diagrams, ray fans and an MTF estimate, bend a singlet, design an achromatic doublet, and export the prescription as CSV or JSON — with a full-screen layout.
Tool ·
Linkages and mechanisms
Mechanisms you can play with — an animated four-bar linkage with the Grashof check, its type, the coupler curve and the transmission angle; slider-cranks with stroke and quick return; disc cams with uniform, harmonic, cycloidal and 3-4-5 motion, pressure angle and undercut check; a 2- or 3-link robot arm you drag by the hand, with both inverse-kinematics solutions; and differential-drive kinematics and odometry for small robots.
Tool ·
Mode S and ADS-B decoder
Decode 1090 MHz Mode S and ADS-B messages field by field — CRC and parity, callsign, altitude, CPR positions with the maths shown, velocity, Gillham codes and Comm-B — from pasted hex, AVR or Beast frames, or live from your receiver over a WebSocket.
Tool ·
Model evaluation workbench
Evaluate a classifier or regressor from its predictions — paste or upload a CSV, or generate a seeded synthetic model — with confusion matrices (micro, macro and weighted precision, recall and F1, MCC, κ), ROC and precision–recall curves (trapezoid AUC against average precision), lift and gain, a cost-matrix threshold chooser, calibration (reliability diagram, ECE, Brier, Platt and isotonic), class imbalance, per-group fairness, and regression residuals.
Tool ·
Model rocketry
Simulate a model rocket's flight from real motor thrust curves — altitude, speed and acceleration, apogee, the right ejection delay, launch-rod speed and descent under the parachute — check its stability with the Barrowman centre of pressure and a side-view drawing, size the parachute, and look up motor classes and the NAR/Tripoli safety codes.
Tool ·
Polarization
Polarised light, interactively: the polarisation ellipse from a Jones vector, an optical train of polarizers, waveplates and rotators you drag and turn (Jones calculus), Malus's law and the three-polarizer paradox, Stokes parameters on a draggable 3-D Poincaré sphere, the Fresnel equations with Brewster's angle and total internal reflection, calcite's double image, waveplate thickness, computed interference colours with a Michel-Lévy chart, photoelastic stress fringes, and how sunglasses, LCD pixels and 3-D glasses work.
Tool ·
Sensor data logger
Log a sensor for a science project from an Arduino, ESP32, Pico or micro:bit over USB (Web Serial) or Bluetooth, or from a simulated source: CSV, name:value, JSON and Serial Plotter lines plotted live with zoom and scroll, markers, per-channel statistics, units and calibration, the sample rate, recordings saved in your browser, CSV/JSON export, and example programs to copy.
Tool ·
Telescopes and optics
Telescope and eyepiece arithmetic (magnification, focal ratio, exit pupil, true field, useful power, Dawes and Rayleigh limits, limiting magnitude, Barlows and reducers), a camera on a telescope (arcseconds per pixel and sampling), binoculars, an interactive ray-tracing bench where you drag lenses and mirrors and watch images form, the lensmaker's equation and Snell's law with total internal reflection.
Tool ·
Wave optics lab
An interactive wave-optics lab: Young's slits and gratings, thin-film colours of soap bubbles and coatings computed spectrally (transfer-matrix method, CIE 1931 colour), Michelson and Fabry–Pérot interferometers, Newton's rings, the slit and Airy patterns with the Rayleigh criterion, any aperture's diffraction pattern by 2-D FFT (draw your own), Fresnel diffraction with the Cornu spiral, a grating spectrometer, and a ripple tank simulation.
Tool ·
Batch, tolerance and shelf life
Break-even between making processes on a log quantity axis, worst-case and root-sum-square tolerance stack-up, Cp and Cpk from pasted measurements with a histogram, surface roughness by process against a bacterium and the 0.8 µm hygienic line, and ASTM F1980 accelerated-ageing times.
Tool ·
Biosignal analysis
Load an ECG, PPG or EMG recording (CSV, PhysioNet WFDB, EDF) or a synthetic sample, filter out wander and mains, detect ECG beats with Pan–Tompkins and correct them, compute RR intervals and HRV, see why a PPG ratio-of-ratios is not an SpO₂ reading, and find EMG onsets — analysis of recordings for learning, not a medical device.
Tool ·
CT and MRI lab
CT reconstruction from scratch (projections, sinograms, Poisson noise, back-projection, FBP and SART), Hounsfield units with window/level, k-space masking, MRI spin-echo contrast, and how a segmentation threshold moves a measured dimension.
Tool ·
Calculus, visually
Drag a secant into a tangent, play the ε–δ game, build f′ from slopes, race Riemann sums, the trapezoid and Simpson's rules on a log–log error plot, paint the area under a curve, and watch Taylor polynomials, linearisation and optimisation work — with every number beside the picture.
Tool ·
Complex numbers, visually
Drag z and w to see addition as vectors and multiplication as rotate-and-scale; modulus and argument with the arctan quadrant trap; Euler's formula with its power series as a spiral of arrows; De Moivre and nth roots; z ↦ wz and z ↦ z² acting on shapes and grids; quadratic roots leaving the real axis; AC phasors and three-phase; and the Mandelbrot set with orbits and the limits of double precision.
Tool ·
Conics, pixels and metrics
Coordinate geometry you can drag: conics from a focus, a directrix and an eccentricity slider (and from slicing a cone), a parabolic reflector, Bresenham, DDA and anti-aliased lines stepped pixel by pixel with the decision value D, Lᵖ unit circles and A* heuristics, the inscribed angle and Thales, a line meeting a circle via the discriminant, and world-to-screen mapping.
Tool ·
Counting, visually
Counting you can see: Pascal's triangle to row 64 coloured mod 2, 3 or 5 with parents and hockey sticks, the binomial theorem as "pick x or y", draggable stars and bars, lattice paths and MISSISSIPPI, an enumerator that shows when a construction counts something twice, derangements and 1/e, next permutation step by step, a backtracking tree with pruning, product-rule stages with password keyspaces, and birthday and hash collisions.
Tool ·
DICOM viewer and de-identification check
Open DICOM files or a folder of slices in the browser — every tag including private ones, flagged against the PS3.15 Annex E de-identification profile; Hounsfield units, window presets, distances in mm and region statistics; what the slice thickness can support; and an anonymised copy with a list of what changed.
Tool ·
Diffusion, dialysis and clearance
Diffusion time t ≈ x²/2D and surface-to-volume 3/r; fit a diffusion coefficient from your own dye-in-agar measurements; dialyser clearance and Kt/V; a week of kidney filtration against haemodialysis; and an animated co-current against counter-current exchanger. Educational simulation only.
Tool ·
Eigenvectors at work: Markov chains, PCA, SVD
Eigenvectors doing real jobs — a Markov chain editor with its steady state and spectral gap (and PageRank), power iteration, Fibonacci by matrix powers against Binet's formula, the Leslie population model, PCA by rotating a line through a cloud, SVD image compression of your own photo with its rank-1 layers, and latent semantic indexing.
Tool ·
Graph algorithms
Draw a graph (or open one of the book's) and step through the classic algorithms one move at a time: degrees, components and Euler trails; the adjacency matrix and walk counts; BFS racing DFS through a maze; Dijkstra and Bellman–Ford (with a negative edge and currency arbitrage); Kahn's topological sort and the critical path; Kruskal and Prim; greedy and bipartite colouring; Hamiltonian tours by brute force against nearest neighbour; and PageRank by random surfers and power iteration.
Tool ·
Half-lives, decay and steady state
A one-compartment model of an invented drug — single or repeated doses, accumulation, steady state after 4–5 half-lives, bioavailability and a loading dose against an invented window band — plus fraction-remaining tables, F-18 and Tc-99m decay with the FDG SUV decay-correction exercise, and hormone half-lives read as time constants.
Tool ·
Health data and medical software
Orientation for health software: place an app in the IMDRF SaMD table, work out k-anonymity from cell counts or a CSV, check the 18 HIPAA Safe Harbor identifiers, build and validate a FHIR Observation (LOINC code, UCUM unit, status, time, subject), explore an HL7 v2 message, tamper with a hash-chained audit log, and fill in a STRIDE table.
Tool ·
Heart, vessels and oxygen
Cardiac output, ejection fraction, MAP and pulse pressure; ΔP = Q × R for the systemic and pulmonary circuits with a pressure cascade; Poiseuille's r⁴ for a vessel, a stenosis or a strap; Dalton, Henry and cylinder arithmetic; and the oxygen–haemoglobin dissociation curve with temperature, CO₂ and pH shifts. Educational simulation only.
Tool ·
Labels, alarms and the senses
Size letters for a viewing distance and a user's acuity (or find how far a label can be read), visual angle in arcminutes, dioptres and reading adds by age, the blind spot, whether an alarm is heard over room noise at a distance, the 3-dB exposure rule, ear-canal resonance and middle-ear gain, two-point discrimination, and a colour-vision and blur check of a photo of your label.
Tool ·
Levers, moment arms and contact
Drag an idealised elbow model and watch the perpendicular moment arm, the cord force (with and without the forearm's own weight) and the cord travel change through the sweep, with the lever class and every assumption listed — plus average contact pressure with everything it cannot tell you, and the energy of a fall.
Tool ·
Number theory step by step
The working behind the answers — Euclid as a trace table and as square tiles, extended Euclid with back-substitution, the two-jug puzzle, an animated sieve, trial division, clock arithmetic and its cardioids, mod-m tables, % on negative numbers, square-and-multiply against naive powers, repeating decimals, LCGs, check digits, Diffie–Hellman and RSA.
Tool ·
Project worksheets for medical makers
The reusable worksheets from Human Biology for the Medical Maker as one fillable, versioned project file — brief with a need-statement checker, evidence separation, task map, constraints sweep, hazard chain ranked by judgement (no scores), requirements with a de-adjective helper, test and version records with change impact, a traceability matrix that shows the gaps, learning objective with a Bloom check, bench-result sentence and handover checklist. Saves in your browser; exports Markdown, CSV and JSON; prints cleanly.
Tool ·
Root finding, step by step
Bisection, Newton, secant and fixed-point iteration side by side, one step per click, with tangents, secants, a cobweb diagram, an iterate table and a log error plot; Newton's failures (flat tangents, cycles, divergence), basins of attraction, the complex z³ − 1 fractal, and Babylonian square roots digit by digit.
Tool ·
Sampling and simulation
Watch probability and statistics happen: the central limit theorem from any distribution (even one you draw), the law of large numbers, confidence-interval coverage, A/B test planning and the cost of peeking, the bootstrap, permutation tests, Simpson's paradox, multiple comparisons, Monty Hall, two-dice events, balls into bins, coupons, inverse-transform and reservoir sampling — all on a seeded generator, so every picture can be linked.
Tool ·
Sets, relations and quantifiers
Paint a three-set Venn diagram from an expression (or find the expression from a painting), linked to its truth table, with inclusion–exclusion counts; explore relations on up to eight dots — reflexive, symmetric, antisymmetric and transitive with witnesses, closures, equivalence classes and Hasse diagrams; and play the ∀∃ against ∃∀ game over a finite domain.
Tool ·
Surfaces, gradients and gradient descent
Type f(x, y) and see a rotatable 3-D surface, contours and a heat map, linked; partial derivatives as slices; the gradient field and a directional-derivative dial; the tangent plane and its error; critical points classified by the Hessian; Lagrange multipliers with λ as a shadow price; a double integral as columns that refine; and an optimiser race of gradient descent, momentum and Adam.
Tool ·
Test accuracy and risk
A diagnostic test's 2×2 table from counts or from sensitivity, specificity and prevalence, drawn as 1,000 people; PPV and NPV against prevalence; ROC curves with a threshold slider and AUC; alarms as a low-prevalence test; relative versus absolute risk and NNT; and why reference ranges flag healthy people.
Tool ·
Test lung and breathing mechanics
A simulated test lung: pressure, flow and volume waveforms from the equation of motion in volume and pressure control, time constants and breath stacking, a lung-volumes spirogram, dead space, airway radius to the fourth power, and Laplace's law. Educational simulation only.
Tool ·
The maths of machine learning
The mathematics under machine learning, hands on — least squares with draggable points (residual squares, outliers, L1 vs L2, normal equations vs gradient descent and SGD), logistic regression and its cross-entropy bowl, a computation graph with forward and backward passes against dual numbers and finite differences, TF-IDF and BM25 search, entropy with a Huffman tree builder and KL divergence, and softmax temperature with an attention matrix.
Tool ·
Tissues, materials and temperature
Tissues against engineering materials on one log scale of stiffness and strength, with the stress-shielding ratio; polymer glass-transition and service temperatures against laundry and steam-sterilisation temperatures, with the evidence gaps each figure leaves; and thermal expansion with the borosilicate versus soda-lime glass comparison.
Tool ·
Ultrasound, Doppler and dose numbers
Pulse-echo depth, wavelength, depth limit and frame rate; reflection at impedance boundaries; the Doppler shift and how an angle error moves the velocity; ultrasonic ranging in air; effective dose against natural background; Beer–Lambert, inverse square, and √N counting noise.
Tool ·
Unit circle and waves
Drag round the unit circle and watch it unwrap into sin and cos, with quadrants, reference angles and exact values; find every solution of sin x = k; see radians as arc length and sin θ/θ → 1; fit A sin(B(x − C)) + D to the book's daylight and tide data; watch simple harmonic motion as the shadow of circular motion; and aim a turret with atan, atan2, y-down screens and the degrees bug.
Tool ·
Unit-safe clinical arithmetic
Clinical unit arithmetic that refuses a number without its unit — glucose, creatinine, BUN, HbA1c and any substance by molar mass; % w/v to mmol/L to mOsm/L; pressure; creatinine clearance with a unit-error demonstration; an infusion error drill on invented scenarios; insulin strengths; and body surface area per kilogram.
Tool ·
Where floating point bites
Watch rounding error happen: the V-shaped error of forward, central and complex-step derivatives in float16, float32 and float64; the quadratic formula losing digits and its stable rewrite; (1 + 1/n)ⁿ collapsing to 1; summation order and Kahan's cash register; Horner versus naive evaluation; forward versus backward recurrences; an ill-conditioned 2×2 system; partial pivoting; and Runge's phenomenon.
Tool ·
Algebra step by step
Solve linear equations, inequalities, quadratics and simultaneous equations with every step explained; divide and factor polynomials; explore a quadratic in four synchronised views with a draggable vertex, watch its roots move through the complex plane, draw sign charts for quadratic and rational inequalities; slide a, b, h and k to transform a graph; and practise with generated problems that check your answers.
Tool ·
Linear systems, visually
Enter a system of linear equations and see it — lines in 2-D, planes in 3-D — then solve it yourself with exact row operations (swap, scale, add a multiple) with undo, hints and "show me", while the picture updates. Classifies one / none / infinitely many solutions, and shows Cramer's rule and least squares. Plus linear programming with a sliding objective line, and an ill-conditioning demo.
Tool ·
Matrix transformations
See what a 2×2 or 3×3 matrix does: the grid, the unit square or cube, the basis vectors and a shape move live as you edit entries or drag the columns — animated from the identity, with the determinant as signed area or volume, eigenvectors, composition, the inverse, presets, the SVD as rotate–stretch–rotate, rotation about a pivot with 3×3 homogeneous matrices, and a neural-network layer folding the plane with ReLU.
Tool ·
Vectors playground
Drag vectors in 2-D or a rotatable 3-D view and watch sums, linear combinations, dot and cross products, norms and Lᵖ circles, span and linear independence, and change of basis update live — with every number beside the picture — and see why random directions in high dimensions are nearly perpendicular.
Tool ·
PID loop simulator
Simulate a PID controller on a first- or second-order plant with dead time — step response, overshoot, settling time, a load disturbance, output limits and anti-windup — get gains from Ziegler–Nichols, Cohen–Coon or SIMC tuning rules, copy the controller as C code, and play with a toy glucose loop to see what sensor and actuator delays do.
ElectronicsElectronicsSoftware engineeringBiology and medicine
Tool ·
Neural network designer
Build a multi-layer neural network from a palette, see every tensor shape and parameter count, draw it, train small ones live in the browser, and generate runnable PyTorch, Keras 3, JAX/Flax or plain NumPy code.
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Big-O explorer and benchmark
Compare growth curves, see how big an input fits a time budget, benchmark your own JavaScript to find its complexity class, look things up in a colour-coded Big-O cheat sheet, watch sorting algorithms run, and see where the costs come from: Fibonacci call trees, recursion trees, binary-search halving, and amortised appends — and why attention is O(N²) in context length, what an SSM's O(N) buys, and what a KV cache saves. Then revise for interviews: name the complexity of code snippets, drill data-structure operation costs, and solve recurrences with the master theorem.
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Boolean logic
Truth tables with a column for every sub-expression, push negations inward one named law at a time, brute-force SAT on CNF clauses, Quine–McCluskey minimisation with Karnaugh maps and gate diagrams, equivalence checks, and register bitfields.
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Chemistry: formulas and the periodic table
Molar mass and percent composition from any formula (hydrates, ions, nested brackets), mass ↔ moles ↔ particles, empirical formulas, an equation balancer that handles ionic and redox equations, an interactive periodic table, and electrochemistry: galvanic cell EMF from standard electrode potentials and Faraday's law for plating and corrosion.
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DNA, RNA, and protein sequences
Paste a sequence or FASTA: composition and GC%, complements, translation in six frames with any genetic code, ORFs, codon usage, restriction sites and virtual digests, primer Tm (nearest-neighbour), and protein MW, pI, extinction coefficient, and hydropathy.
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Floating-point inspector
See exactly how float64, float32, float16, bfloat16, TF32, the FP8, FP6, and FP4 formats used for AI, and the E8M0 scale store a number — and how block-scaled formats (OCP MX, NVIDIA NVFP4, NF4) build a tensor from tiny elements and shared scales.
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Fluid flow and pipe pressure drop
Reynolds number and Darcy–Weisbach pressure drop with Colebrook, Swamee–Jain, or Haaland friction factors and fitting losses; Hagen–Poiseuille laminar flow with an r⁴ sensitivity plot; pipe sizing from flow and velocity; Bernoulli solver; hydrostatic pressure and buoyancy; pump power and orifice flow — with unit-aware inputs.
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Fourier series
See how sums of sines build any periodic function: coefficients and partial sums for square, sawtooth, triangle, custom, or hand-drawn waves, the Gibbs phenomenon and Fejér smoothing, amplitude and phase spectra, rotating epicycles, a draw-any-shape complex Fourier demo, the DFT as arrows that line up or cancel, and the N² against N log N cost of the FFT.
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Genetics: Punnett squares and Hardy–Weinberg
Punnett squares for mono-, di-, and trihybrid crosses with phenotype and genotype ratios (complete, incomplete, or codominance), X-linked crosses, Hardy–Weinberg with a χ² test, carrier frequency from incidence, recessive-disease pedigree risk, and recombination frequency ↔ map distance.
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Geometry: triangles, circles, polygons, solids
Solve any triangle from three values (including both answers of the ambiguous SSA case) with a drawing; arcs, chords, and rise; circle through three points; regular polygons with mitre angles; volumes and surface areas of solids; and coordinate geometry with shoelace area.
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Grammar and parser playground
Write a PEG grammar, parse input with it live, and inspect the result tree, JSON, tokens, and rule cross-references — then download the generated parser. Or see one expression parsed under five precedence conventions — PEMDAS, implied multiplication, Python, C and Excel — as trees.
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Graphing calculator
Plot functions, parametric and polar curves with live parameter sliders; find roots, extrema, and intersections; show derivatives and integrals; and use a scientific calculator.
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Growth curves
Fit logistic, Gompertz, and Baranyi growth models to OD time courses from a plate reader, get lag time, μmax, doubling time, and maximum OD for every well with replicate summaries, and plan cell-culture passaging with seeding densities and split ratios.
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Isotope patterns and exact mass
Monoisotopic, average, and nominal mass for any formula; the isotope distribution as a stick spectrum at unit or fine resolution; m/z for common ESI adducts; and ppm mass error.
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Lab calculations for biology
Haemocytometer counts and seeding, doubling time, centrifuge RPM ↔ ×g, PCR master mixes, A260 quantification and purity, copy number, ligation ratios, oligo resuspension, OD600 → cells, unit conversions, and growth arithmetic: PCR efficiency, exponential growth, tumour doublings, and log reduction, D-values and the sterility assurance level.
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Matrix calculator
Linear algebra with exact fractions or decimals — products (stepped row × column), determinant, inverse, rank, RREF step by step, Ax = b, null space, LU, QR, eigenvalues and eigenvectors (with the 2×2 procedure by hand), norms, and condition number.
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Molecule viewer (SMILES)
Type a SMILES string, a molecular formula or a name (about 630 molecules built in, plus PubChem search) to draw the 2D structure and get the formula, masses, rings, H-bond donors and acceptors, rotatable bonds, TPSA, cLogP and the Lipinski and Veber rules — plus, with RDKit in WebAssembly, canonical SMILES, InChI/InChIKey, exact descriptors, SMARTS substructure search and fingerprint similarity. Load a protein from the Protein Data Bank by ID (1A3N haemoglobin, 4INS insulin) in 3-D and export it as an STL for printing.
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Number theory
Arbitrary-precision integer tools — primality, factorisation, divisor functions, GCD and modular arithmetic, the Chinese remainder theorem, bases, repeating decimals, continued fractions, big factorials, and Roman numerals.
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ODE solver and phase portraits
Solve systems of ordinary differential equations with Euler, RK4, or adaptive Dormand–Prince RK45; see time series and phase portraits with direction fields, nullclines, clicked trajectories, classified equilibria, and a rotatable 3-D view. Plus a slope field with Euler's method against the exact solution, and an integrator shoot-out showing energy drift.
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Orbital mechanics
An n-body gravity simulator with presets (Sun–Earth–Moon, inner planets, the figure-eight three-body orbit, a binary star, a Jupiter Trojan), plus Hohmann transfer, Kepler's-law, escape-velocity, and orbital-element calculators.
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Physics calculators
Physical constants and calculators for kinematics, projectiles with air resistance, oscillations, forces on an incline, collisions, waves and sound, lenses and refraction, the eye in dioptres (far point, accommodation by age, reading add), heat, gases, and orbits.
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Plasmid map
Paste a GenBank record or FASTA and get a circular plasmid map with feature arcs and single/double cutters, edit and auto-annotate features, run virtual digests on a simulated gel, and export SVG, PNG, GenBank, or FASTA.
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Probability: dice, cards, Bayes
Exact dice distributions with a chart; exact permutations and combinations; poker and lottery odds; the birthday problem; binomial, hypergeometric, geometric, and Poisson; Bayes with a natural-frequency tree and icon array; Bloom filters; a naive-Bayes spam filter; series/parallel reliability; expected value and Monte Carlo.
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Programmer's calculator
Integer expressions with hex, binary, and octal; 8- to 128-bit words; signed or unsigned; bitwise operators, rotates, and a clickable bit grid; an n-bit overflow clock with signed and unsigned labels; and what n bits hold, with the KB versus KiB gap.
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Room acoustics and sound
Decibel addition and background correction, inverse-square distance loss, room modes with a chart, RT60 by Sabine and Eyring from a materials table, speed of sound and wavelength, note ↔ frequency with adjustable A4, and a tone, noise, and sweep generator.
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Sequence alignment
Global (Needleman–Wunsch), local (Smith–Waterman), and semi-global alignment of DNA or protein with BLOSUM/PAM matrices and affine gaps; colour-coded output, identity and similarity, the DP matrix with its traceback, and a dot plot.
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Solutions and lab maths
Make up solutions by weight, convert between molarity, % w/v, % w/w, ppm, molality and normality, plan dilutions and serial dilutions, calculate pH, design buffers, solve the ideal gas law and limiting-reagent problems, work out osmolarity and tonicity (van 't Hoff factor, permeant solutes), and do the available-chlorine arithmetic for disinfectant tablets.
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Spectroscopy and calibration curves
Beer–Lambert solver with absorbance ↔ transmittance, a calibration-curve fitter (linear, through zero, or quadratic) with R², LOD/LOQ and back-calculated unknowns, and light conversions between wavelength, wavenumber, frequency, and photon energy with the visible colour.
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Spectrum analyser
Generate, load, or record a signal and analyse it: waveform, FFT spectrum with window functions and averaging, peak detection, an STFT spectrogram, and THD / THD+N / SINAD for a test tone — plus synthetic ECG, EMG, EEG and PPG with mains hum, baseline wander and noise, and a signal-averaging demo.
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Statistics
Paste data and get descriptive statistics, histograms and box plots, regression with R² and residuals, correlation matrices, distribution calculators, and hypothesis tests with plain-language results.
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Survival analysis
Kaplan–Meier curves with Greenwood confidence bands, median survival, a number-at-risk table, log-rank (and Gehan–Breslow, Tarone–Ware) tests for two or more groups, and Mantel–Haenszel hazard ratios — from a time, event, group CSV.
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Symbolic algebra
A computer algebra system in the browser: simplify, expand, factor, solve equations and systems, differentiate, integrate, take limits and Taylor series, partial fractions, and substitution — with LaTeX output, a step history, and a plot.
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Thermochemistry
Reaction enthalpy, entropy and Gibbs free energy from standard formation data, with ΔG and K against temperature, Hess's law solved automatically, ΔG° ↔ K and van 't Hoff, calorimetry, and bond-enthalpy estimates.
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Titration curves
Simulate acid–base titration curves exactly for strong, weak, polyprotic, and mixed acids and bases, find equivalence and half-equivalence points and buffer regions, choose an indicator by titration error, and analyse your own pH-meter data by derivative and Gran plots.
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Unit converter
Convert between hundreds of units — length to radiation dose — or type a query like “3.5 ft·lbf to N·m” and let dimensional analysis do the rest.