Don’t memorize it.
Play with it.
play2lrn turns the concepts that never quite stick — ad auctions, projectile motion, search intent — into simulations you can drag, break and replay. Move one control and the idea explains itself.
Read it. Re-read it. Highlight it. Forget it.
- A definition you can recite but not use.
- A diagram that never moves.
- A worked example with someone else’s numbers.
- Thursday, and it’s gone.
Grab a control. Break the thing. Now you know.
- Every variable is a slider you can move.
- The output redraws the instant you touch it.
- Your numbers, your experiments, your mistakes.
- Understanding you can rebuild from scratch.
Pick a shelf. Start with any simulation.
New simulations land regularly — search or filter by category to find one.
World Clock
Track the current time in cities around the world. Add or remove cities, switch every clock between analog and digital faces, toggle 12/24-hour format, and watch day and night sweep across the time zones in real time.
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States of Matter
A particle model of solids, liquids, and gases. Add or remove heat and watch how spacing, bonding, and speed change as the substance crosses its melting and boiling points. Switch between a friendly illustrative model and a real Lennard-Jones argon model.
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Le Chatelier Equilibrium Shifter
A single-equilibrium teaching model of Le Chatelier's principle. Pick a reaction (Haber process, ester formation, or salt dissolution) and change its temperature, total pressure, or any starting concentration. A van 't Hoff relation moves K with temperature; a gas-mole pressure term and a bisection solver find the reaction extent that restores Q = K, then a tilting two-pan balance, live Q / K meters and an animated composition chart show which way the mixture shifts and by how much. Illustrative — activities are approximated by molar concentrations.
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Ad Fatigue Simulator
An illustrative media-planning model of the trade-off between reach, memory, response, and fatigue. Set a frequency cap, audience, budget, creative rotation and relevance, then step through a 10-week campaign and watch recall, conversions, fatigue and cost per conversion move together.
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AIDA Marketing Funnel
An interactive AIDA funnel: a starting pool of prospects moves through Awareness, Interest, Desire and Action by the conversion rate you set between each pair. Adjust the audience or any rate and every stage below recalculates live. Click a stage for its channels and KPIs, or run the guided tour.
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Attribution Modeller
A fixed customer journey across paid social, retargeting, video, email and search. Switch between first-click, last-click, linear, U-shaped and time-decay attribution and watch the same order value redistribute credit across the touchpoints. Adjust the number of journey steps and the time-decay half-life.
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CAC vs. LTV
A month-by-month cohort simulation of a subscription business. CAC is spent in cash the day a customer is acquired; LTV is collected slowly against monthly churn. Adjust growth, unit economics, starting cash and opex — and see how a healthy LTV:CAC ratio can still empty the bank account, and when a funding round would rescue it.
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E-commerce Funnel Simulator
A search-ads e-commerce funnel from spend to profit. An ad budget and cost-per-visit buy the traffic; four sequential conversion rates (visitor → product page → cart → payment → purchase) decide how many people actually buy. See revenue, ROAS, cost per purchase, contribution margin, break-even ROAS and net profit update as you move any input — with loss-making, break-even and profitable scenarios to start from.
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Facebook Organic Algorithm Simulator
An illustrative model of the Facebook Feed ranking signals Meta has publicly described for 2025–2026: relationship strength, format, same-day recency, poster trust, weighted engagement (private shares > comments > likes), and content-quality demotions. Tune one post's format, timing, audience and predicted engagement, watch a three-post feed re-rank live, and read a factor-by-factor breakdown of what boosted or hurt its reach. Built from public documentation — not Meta's real weights.
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How Search Engines Work
An animated six-stage walkthrough of the pipeline behind every search: crawling (bots discover pages by following links), rendering (HTML is parsed into a DOM tree and key elements extracted), indexing (words are tokenized into an inverted index), query processing (a search is corrected, expanded and matched to candidates), ranking (candidates are scored on relevance, authority, speed, mobile, freshness and engagement, then sorted), and the SERP (the sorted list is assembled with featured snippet and 'people also ask'). Step through it or press play. Illustrative model — not any engine's real weights.
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Meta Andromeda Ads Algorithm Simulator
An illustrative model of Meta Andromeda — the retrieval stage in front of ad ranking, the auction and delivery pacing that powers Advantage+. Using a worked example (affordable 3 BHK flats sold to one mixed city-wide audience), set format, objective, creative quality, hook diversity, audience breadth, bid and budget, then watch the retrieval-and-ranking funnel, an embedding match gauge, per-creative 'entity' coverage, relevance diagnostics, a sample Total-Value auction and a Monte-Carlo daily dashboard all recompute live. Flip between Andromeda and legacy two-tower retrieval to see how much of the result depends on the engine itself. Built from Meta's public engineering write-ups and third-party analysis — not Meta's real weights.
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The Messy Middle
An animated walkthrough of Google's 'Messy Middle' framework: the space between a purchase trigger and the decision, where a buyer doesn't move in a straight line but loops back and forth between broad exploration (search, YouTube, Reddit, social) and focused evaluation (comparison sites, configurators, reviews, charging maps, incentive and finance calculators, a test drive). Step through a 17-touchpoint EV journey or press play; each stop shows what the buyer is doing, why it matters for marketers, and a running count of how many times they've crossed between the two mindsets. Illustrative single journey, not an exhaustive map.
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POEM Growth Simulator
An illustrative scenario model of the Paid / Owned / Earned media framework over time. Set a monthly budget, planning horizon, starting point, priority, market and content quality, then slide the paid vs. owned split (earned is the remaining enablement budget). A month-by-month simulation shows reach by channel and estimated conversions, budget deployment, and a narrative read on whether the plan is a fast launch or a durable growth engine. Flip on the month-13 spend pause to see what owned assets and earned credibility keep delivering once paid stops. Teaching model of the trade-off — not a media forecast.
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Display Programmatic Advertising
An animated 10-step walkthrough of a real-time bidding (RTB) auction — the automated process between a page loading and an ad appearing. Pick a publisher and whether the ad exchange has audience data, then step (or play) through the flow: the page opens an ad slot, the SSP sends a bid request, the exchange enriches it from a DMP, three DSPs each evaluate and bid for their advertiser, a second-price auction picks the winner and clearing price, and the winning creative is served back and rendered. A flow diagram, a live bid board, an event timeline and a glossary update at every step. Fictional players and bid values — illustrative of RTB mechanics only.
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Search Ad Auction Simulator
A teaching model of the Google-style search ads auction. Write an ad — keyword, bid, headlines, description, landing-page keywords, load time, mobile, assets — and watch a transparent proxy turn those signals into Expected CTR, Ad relevance, Landing page experience and a 1–10 Quality Score, then into a teaching Ad Rank (bid × QS × asset & competitiveness modifiers). Your ad is ranked live against four fixed competitors on a mock results page, with a display threshold that a low bid or low quality can both fail. Shows why a higher-quality lower bid can outrank a weaker higher bid. A teaching proxy, not Google's real auction or weights.
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Search Intent Classifier
A keyword-rule teaching model of the four classic search intents: informational (learn or solve), navigational (reach a specific site), commercial (research options), and transactional (ready to act). Type any query into the analyzer and it names the strongest intent signal, highlighting the words that drove the call; a five-question quiz tests your read of new queries; and a 'wording effect' panel puts near-identical searches side by side to show how adding 'buy', 'best', a price or a place moves the searcher from one stage to the next. A first-pass heuristic — real searches are often mixed, and human context beats a keyword rule.
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Supply & Demand Equilibrium
A linear-curve model of a single competitive market. Slide the demand and supply shifters and watch the equilibrium — the crossing point where quantity demanded equals quantity supplied — move: a demand increase raises both price and quantity, a supply increase raises quantity but lowers price. Toggle a price explorer to hold the market away from equilibrium and see a shortage (excess demand) or surplus (excess supply) open up, or shade in consumer and producer surplus to see the gains from trade — and how a shortage destroys some of them. A simplified illustrative model, not a calibrated forecast.
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Greenhouse Effect Simulator
A simplified radiative-forcing climate model. Adjust atmospheric CO2, methane and nitrous oxide, the sun's output and Earth's reflectivity, and watch total radiative forcing, the modeled equilibrium surface temperature, and a factor-by-factor breakdown respond. An energy-balance diagram shows how many of five outgoing infrared rays escape to space versus getting trapped and re-radiated down. Presets cover pre-industrial 1750, today, a high-emissions pathway and an ice age. Uses the standard IPCC AR5 simplified forcing formulas with a climate sensitivity of 0.8 degC per W/m2 - an equilibrium estimate for teaching, not a forecast.
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Compound Interest Explorer
A month-by-month savings-growth model. Set an initial amount, a monthly contribution (which can grow each year with your raises), a rate, a horizon, a compounding frequency and whether you deposit at the start or end of each month. A stacked chart splits every balance into the money you paid in versus the interest it earned, and marks the crossover year where growth overtakes deposits. A two-investors panel shows the cost of waiting — how far behind a delayed start leaves you and the monthly top-up it would take to catch up — and an optional panel compares two compounding frequencies. Educational only; assumes a constant annual return, which real markets never provide.
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Blood Sugar After a Meal
A simplified, illustrative model of the post-prandial ('after eating') blood-glucose response. An absorption pulse whose shape is set by the food's glycaemic index feeds a first-order clearance term back toward a fasting baseline, and that clearance rate is scaled by sleep quality, meal timing and — while you move plus a fading window afterward — post-meal activity. Pick a food, portion, activity and when you start it, your sleep and the time of day, and read the peak, the time to peak, the time back to baseline and the area under the curve, with an optional overlay of the same meal without exercise. Presets cover a worst case, a typical meal and a best case. A teaching diagram with hand-tuned parameters — not fitted to clinical data, not medical advice.
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Calories, Activity & Weight Trends
A day-by-day energy-balance simulator. Set body stats, calorie intake and activity, and watch weight respond over weeks or years: each day BMR is recomputed from the current weight, scaled by a metabolic-adaptation factor that ramps toward a 15% ceiling during a sustained deficit, then combined with lifestyle activity, structured exercise and the thermic effect of food into TDEE; the day's calorie balance moves weight by balance divided by 7,700 kcal per kg. A weight chart overlays the simulated trend, a noisy scale reading and the naive linear projection; a stacked chart splits the daily burn into BMR / lifestyle / exercise / digestion; a diverging chart shows the weekly deficit or surplus. Snapshot up to two scenarios to compare, and switch intake partway through to model a diet break. Educational only, not medical advice.
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How Infection Spreads
An agent-based outbreak playground, a variant of the classic SIR model. Dozens of dots wander a shared space; an infectious dot near a susceptible one transmits with a probability set by contagiousness, and contact rate controls how often those encounters happen. After a detection delay, sick dots may be isolated into a quarantine pen; prior immunity and vaccination start a share of the population already protected; an optional mortality rate makes the illness fatal. Live sliders change the running outbreak instantly, setup sliders restart it, and a stacked epidemic curve tracks the whole population over time alongside R0, effective R and the herd-immunity threshold. One-click presets cover no precautions, social distancing, isolating the sick, a vaccination drive and a full response. A simplified illustrative model, not an epidemiological forecast.
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How the Immune System Trains
An interactive model of how vaccines build immunity. One simplified ODE engine runs three side-by-side scenarios against the same pathogen: an unprepared naive first infection, a vaccination that teaches the immune system safely, and a later real exposure that starts with the memory and antibody left over from that vaccination, decayed across a chosen time gap. Live controls set pathogen virulence, exposure dose, vaccine type (mRNA, inactivated, live-attenuated or subunit), an optional booster, the re-exposure gap and the simulation length. Each panel shows an activating cell cascade, a particle battlefield, live readouts and an event timeline; three overlaid charts track pathogen load, antibody titer and memory-cell strength, and a summary table compares days-to-clearance, peak titer, illness burden and final memory strength. Six guided experiments surface one concept each — the power of memory, why boosters matter, waning immunity, and more. An educational illustration of primary vs. secondary immune responses, not clinical data or a specific product.
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How a Pendulum Works
A live simple-harmonic-motion lab. Two independent pendulums and one spring oscillator share a stage; a scrolling displacement-time trace overlays all three so you can watch them drift apart or stay locked. Each pendulum has its own string length, bob mass, release angle, starting push, gravity and damping, and integrates the full non-linear equation of motion with RK4 — so a wide release genuinely runs slower than the small-angle formula and its trace is not a perfect sine. The spring follows T = 2π√(m/k), the deliberate contrast: for a pendulum mass does nothing, for a spring it sets the tempo. Readouts show each pendulum's predicted vs. live-measured period, their percentage gap and the spring period. One-click presets (mass, angle, length, planet hop), a gravity dropdown for Moon/Mars/Earth/Jupiter, copy-between-pendulums buttons and ten guided experiments round it out. An educational model, not a metrology-grade simulator.
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How Projectile Motion Works
A launch-and-watch kinematics lab. Velocity splits into independent horizontal and vertical components: with no drag the horizontal speed stays constant while gravity alone bends the vertical, tracing a parabola. Turn on air resistance and a quadratic drag force −b·|v|·v curves the real path below and short of the dashed ideal curve, with the gap widening as speed². A live preview redraws the predicted arc, launcher angle and axis scale as you drag the controls; Launch runs the flight with adjustable playback speed, optional velocity-vector arrows (vₓ, v_y and resultant) and live readouts for time, position, speed, components and peak height. An optional Projectile B shares every setting with A except one isolated variable — speed, angle, height or gravity (Earth, Moon, Mars, Jupiter or custom) — for a clean controlled comparison, and trajectories can be pinned to compare several launches at once. Ten guided experiments cover the 45° range myth, complementary angles, why height shifts the best angle, v² scaling, and how drag reshapes the arc. An educational model, not a ballistics calculator.
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Relativity Playground
Seven hands-on experiments that let you discover Einstein's relativity before you see a single equation. Chase a light beam and find you can never gain on it; race two clocks and watch the moving one fall behind (then see why, with a bouncing-photon light clock); shrink a spaceship by speeding it up and flip reference frames to see who measures what; replay Einstein's lightning-and-train experiment to lose the idea of a universal 'now'; send a twin to a distant star and reunite them years apart; park clocks near Earth, a neutron star and a black hole to see gravity slow time; and connect it all on an interactive spacetime diagram. Predict-before-reveal questions, challenges, a relativity-effect meter, a GPS real-world link and a Simple / Advanced mode that unlocks equations, worldlines and Lorentz-transformed coordinates.
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Unit Economics Explorer
A hands-on pricing simulator for a subscription business. Drag price, cost, conversion, acquisition cost, churn and traffic and watch the whole cascade react in real time, then read the payoff on a profit-vs-price 'mountain' and a 24-month cash projection. Switch between three preset businesses (a coffee club, a SaaS app, a meal kit), chase a challenge to find the peak-profit price, or work through ten guided experiments that isolate exactly what each lever controls.
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Earth's Seasons Simulator
A working model of Earth's yearly trip around the Sun. Change the axial tilt, drag Earth along its orbit (or press play), and pick a latitude to stand at, then watch an orbit view, a 3-D globe, a noon-Sun 'flashlight test' and a year-long daylight graph all update together. See noon Sun height, day length, sunlight received and distance to the Sun for your spot, complete five hands-on missions, and discover why Earth's tilt — not its distance from the Sun — is what actually causes the seasons.
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Market Crash Lab
An agent-based stock-market simulator: 60 investors each hold one $100 stock, and a news shock sets off a feedback loop between fear, panic selling and margin calls. Tune selling pressure, leverage, sentiment and market liquidity, watch the price chart, the crowd of investors, and a live doom-loop diagram react together, then read a report on how much of the fall came from news versus panic versus forced selling. Ten ready-made scenarios (from Calm & cash to Perfect storm) let you compare runs side by side.
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Wave Interference Explorer
Tune the frequency, amplitude, phase and wavelength of two travelling waves and watch superposition happen live: a snapshot of both waves along a string plus their sum, one spot's motion traced over time (with its beat envelope), and a top-down ripple tank with two draggable sources showing bright constructive lanes and calm nodal lines. A status banner and live numbers (phase difference, beat frequency, peak combined height, wave speed) explain what kind of interference is happening, and ten presets — from Team up and Cancel out to Beats, Octave and Stretch mismatch — jump straight to the key ideas.
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Lens Lab
Drag a candle toward and away from a convex or concave lens and watch the ray diagram redraw live: the parallel, centre and focal rays, the real or virtual image they form, and badges that say whether it is inverted, upright, larger or smaller. Tune the focal length and the object distance, switch on the virtual ray guides, and read off the image distance, magnification and lens power from the thin-lens equation. Four presets — camera, eye, microscope and spectacles — show how familiar devices put a lens to work.
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Electric Circuit Playground
Build a circuit with one to three resistors, wire them in series or in parallel, and turn the battery voltage up and down. A live diagram shows charge flowing (dot speed follows the current), resistors that glow with the power they burn, and an ammeter you can trust. Every resistor gets its own voltage, current and power readout, the working for R-equivalent and Ohm's law is shown step by step, and an I–V graph proves the straight line through the origin. Flip the switch to break the loop, or swap conventional current for electron flow.
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Interest Rates vs Bond Prices
Set a bond's face value, coupon rate, maturity and payment frequency, then push the market interest rate up and down. A price-versus-rate curve, a cash-flow chart that shows every payment shrinking to its present value, and a seesaw make the inverse relationship impossible to miss. Live readouts give the price, your paper gain or loss since you pinned a purchase price, the current yield and the duration, while +1% / +2% / −1% / −2% rate-shock buttons reveal why long, low-coupon bonds swing hardest and why the curve bends (convexity).
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Overfitting Playground
Fit a polynomial model to noisy data and play with four dials — dataset size, noise level, model complexity and training epochs — while a live plot shows the curve the model learned against the hidden true pattern and a set of unseen points. A learning-curve chart tracks training accuracy against real-world accuracy epoch by epoch, marks the sweet spot for early stopping, and shades the overfitting zone. Readouts, a generalisation-gap meter and a plain-English verdict say whether the model is underfitting, generalising well or overfitting, and one-click presets jump straight to each case.
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Life Lab: Conway's Game of Life
Draw cells, drop in famous patterns (gliders, pulsars, the Gosper gun, the R-pentomino…) and watch Conway's rules play out live on a wrap-around world. Step forwards and back, switch on the prediction overlay to see which cells are about to be born or die, hover any cell to see exactly why, and follow the population chart as the world boils, cools and settles. Change the birth and survival numbers to invent other universes (HighLife, Seeds, Day & Night, Maze…), turn on mutation to watch sturdy patterns survive, work through eight guided lessons, and try five build-it-yourself challenges.
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Rate Lab
A toy economy you run as central bank governor. Move the policy interest rate (or let a Taylor-rule robot banker do it) and watch it travel down a five-stage transmission pipe — loans, spending, jobs, then prices — each with its own lag, while demand, inflation, unemployment and the town's mood update live on gauges, a history chart and a running headline feed. Throw a spending boom, an oil shock or a confidence crash at the economy, or load one of ten scenarios (from a gentle Recession Rescue to the Volcker Cure and Stagflation) to see why central banks must act early, why effects lag by a year or more, and why overshooting causes recessions.
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Order Book Playground
A live limit order book with a real price-time-priority matching engine. Place market or limit orders against a book of resting bids and asks, watch the rows your order eats highlight in real time, and see the resulting slippage, spread and price impact. Start the market to bring in robot traders and market makers who refill the book after a big trade, tune liquidity from a desert-thin market to a deep ocean, and work through twelve scenarios — from a tiny order in a deep pool to a whale dump, a flash crash and a marketable limit order — that isolate exactly what spread, slippage, liquidity and price impact mean.
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Doppler Effect Playground
An ambulance siren sounds higher as it races toward you and lower once it has passed. Here you drive the siren yourself: sound waves spread out as rings, squeezed together in front of the moving source and stretched out behind it. Drag the ambulance or the listener anywhere, change the source speed, siren frequency and speed of sound, and turn the sound on to hear the pitch the listener actually gets. Readouts show the emitted and heard frequency, the shift, the approach speed and the Mach number, and a pitch meter swings red when the source approaches and blue when it recedes. The sound takes time to travel, so the pitch changes only when the waves reach the listener. Push past Mach 1 to see the waves pile into a shock cone.
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Standing Waves Lab
Shake one end of a rope and the wave you send runs to the far end, reflects and comes back through itself. Most of the time the outgoing and returning waves are out of step and the rope just jiggles. At special frequencies they line up, every round trip adds to the swing, and the rope settles into a standing wave: points that never move (nodes) and points that swing the most (antinodes). Tune the shaking frequency, wave speed, rope length and damping, fix the far end or let it slide on a pole, and show the two travelling waves that add up to the pattern. A live resonance curve shows where the harmonics are and lets you click straight to one, readouts give the wavelength, fundamental, harmonic number and gain, and an optional tone gets louder as you hit resonance.
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Orbital Mechanics Sandbox
Throw a ball sideways from a very tall tower: gently and it falls, harder and it lands farther away, hard enough and the ground curves away as fast as it falls, so it never lands. This sandbox puts a satellite above the Earth and lets you choose its sideways launch speed and launch height. A colour-coded speed slider shows where the crash, orbit and escape zones begin, a dashed line predicts the path before you launch, and live readouts track speed, altitude, orbit shape, closest and farthest approach and the time for one lap. Show the velocity and gravity arrows, shade Kepler's equal areas, and work through ten experiments, from dropping the satellite to parking it in a space-station or TV-satellite orbit.
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Ideal Gas Playground
Gas molecules zoom around a cylinder closed by a piston, each coloured by its own speed, and every bounce off the walls adds to the pressure. Drag the piston to change the volume, heat or cool the gas, and add or remove molecules. Lock any one of pressure, volume, temperature or moles and move another: the gas answers by changing exactly one more so that PV = nRT stays true, with the live numbers plugged into the equation. A graph switches to match what you lock, showing Boyle's hyperbola, or Charles's and Gay-Lussac's straight lines heading for zero at absolute zero, and traces where you have been. A pressure dial, thermometer, wall-hit counter and ten guided experiments cover Boyle's, Charles's, Gay-Lussac's and Avogadro's laws.
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Refraction & Total Internal Reflection
Aim a laser from inside water, glass or diamond (or any refractive index you choose) at the surface. Snell's law bends the escaping beam away from the normal; tilt further and it skims the surface at the critical angle, then vanishes as all the light bounces back: total internal reflection. Drag to aim or auto-sweep, snap to the critical angle, and flip the direction to see why light can always get into a denser material. Live readouts give both angles, the critical angle, the reflected and refracted shares and light's speed in the material, with Snell's law worked through. A reflection chart shows the reflected share climbing to 100%, and an optical-fibre view shows light trapped perfectly past the critical angle or leaking away at every bounce below it. Ten experiments cover everything from a straight-through beam to a diamond's sparkle.
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Bumper Carts: Conservation of Momentum
Two carts with faces roll along a frictionless track and crash. Set each cart's mass and velocity (left or right) and how bouncy the bumpers are, from sticky velcro to perfect springs. Predict what each cart will do, launch, and check your guess. Momentum arrows, a before-and-after table and momentum bars show the carts trading momentum while the total never changes; live graphs of momentum and kinetic energy over time show the total-momentum line staying flat through the crash while energy drops in a squishy collision; and a centre-of-mass marker glides steadily straight through the impact. Ten experiments cover Newton's-cradle swaps, light carts bouncing off heavy ones, sticky crashes, head-on dead stops and more.
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Buoyancy & Density Lab
A tank of liquid where you drop objects and watch them sink, bob or float. Choose the material (cork, wood, ice, aluminium, steel, gold or any density), its mass and its shape (block, ball, or a hollow ship hull you can spread out), and the liquid (oil, water, salty sea, honey or mercury). Weight and buoyancy arrows, force bars, a rising liquid level and a splash show Archimedes' principle at work, and you can grab the object and dip it in by hand. A float-or-sink verdict compares average density with the liquid's, a density scale places your object among real materials and liquids, and readouts give shape volume, displaced liquid, forces and apparent weight. Ten experiments cover why steel sinks, how a steel ship floats, steel floating on mercury and the hover trick.
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Acid–Base Titration Lab
A virtual titration bench: a burette of sodium hydroxide over a flask of acid with indicator. Add base a drop, a millilitre or a steady pour at a time (or let Auto-run do it), and watch the pH meter, the flask colour and the titration curve draw itself. The pH barely moves for most of the run, then a single drop sends it up several units at the equivalence point. Switch between a strong acid (HCl) and a weak acid (acetic), compare phenolphthalein, bromothymol blue and methyl orange, and change the concentrations and volume to move the equivalence point. An 'Inside the flask' panel shows acid being used up and excess base piling up, the weak-acid curve marks the buffer point where pH = pKa, and ten guided experiments build up the whole story.
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Reaction Rate & Collision Theory
A box of A and B particles flies around and collides. Every A–B hit either bounces off (grey ring) or, if it carries at least the activation energy, makes a product AB (green burst). Turn up the temperature, crowd the box or add a catalyst and watch the collision count, success rate and reaction rate respond. A hit-strength chart lays your real collisions over the e^(−Ea/kT) curve, an energy hill shows the catalyst's lower route, a live graph tracks reactions per second, and an Arrhenius builder lets you record the success rate at several temperatures and watch it curve steeply upward. Ten experiments separate 'more hits' from 'harder hits'.
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Radioactive Decay & Half-Life Lab
A box of up to 5,000 unstable atoms. Press play and they decay one at a time: each flashes, spits out an alpha, beta or gamma particle, and turns into a stable daughter atom. You can't predict when any single atom will go (click one to follow it and try), but the graph of atoms remaining always traces the same smooth curve, halving every half-life. Pick a real isotope (carbon-14, iodine-131, technetium-99m, radon-222 or uranium-238) or a custom atom with your own half-life, change the crowd size, and compare runs against the theory curve. Switch the graph to a log scale to turn the curve into a straight line, watch the activity fall in step with the atoms left (A = λN), and turn on the Geiger counter to hear it slow down. A half-life scoreboard, a running coach and ten guided experiments (including carbon-dating a bone) build up the whole idea.
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Electrolysis Playground
Build a small electrolysis cell: a beaker of electrolyte, two electrodes and a battery. Choose copper(II) sulfate, copper(II) chloride, salt water, dilute sulfuric acid or molten lead(II) bromide, and graphite or copper electrodes. Below the minimum voltage the ions only jiggle; push past it and cations drift to the cathode, anions to the anode, and products appear: copper plating, bubbles of hydrogen, oxygen or chlorine filling collection tubes, bromine vapour or a pool of molten lead. Show the electrons in the wire and the conventional-current arrows side by side, swap the battery wires to turn everything around, and read the half-equations for each electrode. Live meters track current, charge and products, a current–voltage graph shows the threshold, a Faraday readout links charge to product, and ten guided experiments cover plating, copper refining, splitting water 2 : 1 and why salt water never gives sodium.
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Solubility & Saturation Lab
A virtual beaker of water and a scoop of salt. Drop in a few grams at a time and watch them dissolve into invisible particles until the water can hold no more; the rest piles up as crystals. Heat the water and more dissolves; cool it and the surplus crystallises back out. A solubility curve beside the beaker shows the limit at every temperature, with a dot marking your solution, so you can see it cross from unsaturated to saturated. Choose potassium nitrate, table salt, potassium chloride, ammonium chloride, blue copper(II) sulfate or cerium(III) sulfate, which dissolves less when it gets hotter. Change the amount of water to crystallise by evaporation, stir to see that stirring changes the speed but not the limit, compare every curve on one graph, and work through ten guided experiments.
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Fourier Series Builder
A sine-wave mixing desk. Sine waves are the smoothest wiggles there are, yet add the right ones together and they build a boxy square wave, a sharp sawtooth or a triangle. Press “Add next sine” (or Auto-build) and watch the coral sum close in on the target, while chained spinning arrows show the same sum as circles within circles. Drag the bars of the spectrum to set any harmonic by hand, show the separate sines underneath, and turn on the sound to hear a pure tone turn buzzy as harmonics pile up. Live readouts track the error, how much of the target you have matched and the stubborn 18% Gibbs overshoot at the jumps, and ten guided experiments explain why the square needs only odd harmonics and why the triangle converges so fast.
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Bayes' Theorem: The Positive Test Paradox
A test comes back positive. How likely is it that you are actually sick? Set how common the disease is (prevalence), how well the test catches sick people (sensitivity) and how well it clears healthy people (specificity), and Bayes' theorem answers live. A crowd of 1,000 or 10,000 dots shows every person, coloured by their true health and their test result. Switch on “Only positives” to see the group a positive result really puts you in. A frequency tree turns the probabilities into plain head-counts, a curve you can drag shows how the answer climbs as the disease gets more common, and a “test again” chain shows why doctors confirm with a second test. Ten guided experiments walk through the base-rate fallacy.
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The Monty Hall Door Lab
The most argued-about puzzle in probability. One door hides a car and the others hide goats. You pick a door, the host opens a goat door, and you decide whether to stay or switch. Play it by hand with “Show chances” on to watch the probability move onto the last closed door. Then let the robot play up to 10,000 rounds and watch the win-rate lines and the tally of squares settle on 1/3 for staying and 2/3 for switching. Change the rules with more doors, a host who only guesses, or a host who opens just one door, and see when switching helps and when it doesn't. Ten guided experiments build the case step by step.
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Linear Regression by Hand
Fit a straight line by hand and find out what “line of best fit” really means. Drag the handles to tilt the line or drag the line to slide it. Every miss between a point and the line is drawn as a real square, and the total area, the sum of squared errors (SSE), is your score. Add, move and delete points, try ready-made data such as a trend, a noisy cloud or an outlier, and see how one far-away point takes over the error bar. Slice charts and a full SSE landscape show the bowl-shaped error surface with exactly one bottom: the least-squares line. Challenge mode hides the score so you can test your eye, and ten guided experiments explore residuals, R², outliers and why the errors are squared.
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Evolution Sandbox: Natural Selection
A small world of fuzzy critters, each carrying three inherited genes: body colour, running speed and fur thickness. Every generation, hawks hunt by day and pick off the critters that stand out against the ground, the climate tests their fur at dusk, and the survivors have babies at night that inherit their genes with small random mutations. Set the environment (forest, desert, snow or volcanic rock), the temperature, the number of hawks, the mutation rate and the population size, then watch camouflage emerge. Trend lines chase their targets, a histogram shows the spread of each trait against the first generation, and Nature's diary narrates every generation. Ten guided experiments explore selection pressure, variation, trade-offs, sudden environmental change and extinction.
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Rabbits & Foxes: Predator–Prey Dynamics
A living meadow of rabbits and foxes driven by the Lotka–Volterra equations. Rabbits breed and get eaten, foxes turn meals into cubs and die off, and the two populations chase each other round an endless lagged cycle. Watch it three ways: the animated meadow, the population chart with automatically measured fox lag and cycle length, and the phase loop with its “no change” lines and balance point (click the loop to drop the populations anywhere). Change the birth, hunting and death rates, add a grass limit or whole-animal extinction, meddle by releasing or removing animals, and take the Stabilise Challenge to see why the lag makes taming the cycle so hard. Ten guided experiments cover the lag, the balance point, Volterra's principle and the extinction trap.
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Punnett Playground: Squares & Inheritance
A virtual breeding lab with four set-ups: a one-gene cross (pea seed colour), a two-gene cross (colour and shape), linked genes on the same fruit-fly chromosome with an adjustable recombination frequency, and sex-linked eye colour on the X chromosome. Choose each parent's alleles, read the Punnett square to see every possible baby and its chance, then press Make babies to roll the genetic dice. Expected and observed ratios sit side by side with a chi-square test of the fit, the babies appear in a seed tray or fly nursery, and any baby can be promoted to parent so you can follow a family from P to F1, F2 and beyond. Ten guided experiments recreate Mendel's 3:1 and 9:3:3:1, test crosses, incomplete dominance, genetic mapping and Morgan's white-eyed flies.
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Osmosis Lab: Cells & Membranes
A virtual beaker with a single living cell wrapped in a semi-permeable membrane. Water molecules slip through the membrane in both directions while the bigger solute particles stay put, and the cell swells, bursts, shrivels or stays the same depending on the solution. Pick pure water, saline, sea water or pickle brine, switch between an animal cell (which can burst) and a plant cell (whose stiff wall makes it turgid or plasmolysed), and change the cell's inside concentration and the membrane's water permeability. Live readouts track tonicity, net water flow, size, wall pressure and every water molecule crossing; a size chart keeps the previous cell's curve for comparison; and Predict-first mode quizzes you before each drop. Ten guided experiments cover lysis, crenation, turgor, plasmolysis and why hospital drips use 0.9% saline.
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Moon Phases & Eclipses Explorer
Two linked views of the Sun, Earth and Moon. In the space view you hover above the North Pole and drag the Moon around its orbit (or drag the little person to change the time of day). In the sky view you stand in London, Quito or Sydney and see the Moon's phase, where it sits in the sky and whether it is day or night. Readouts give the phase, how much is lit, the Moon's age, and approximate moonrise and moonset. A side view of the 5° tilted orbit and a true-scale shadow close-up show why New and Full Moons only sometimes make eclipses, and a 30-day Moon calendar marks the eclipses to come. Animate the days, jump to the next eclipse, tick off ten missions, test yourself with a moonrise quiz and work through ten guided experiments.
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Seasons & Axial Tilt Lab
A hands-on lab for the Earth–Sun system. Tip Earth's spin axis anywhere from 0° to 90°, drag Earth round its orbit or play the year, stand at any latitude, and even stretch the orbit into an exaggerated oval. Six linked views show what changes and why: the orbit from above, Earth side-on with your latitude's day and night arcs, the Sun's path across your sky, the same sunbeam spread over steep or shallow ground, a year graph of day length, noon Sun angle or sunshine (with the opposite hemisphere and real Earth for comparison), and a two-hemispheres card that puts the 'closer to the Sun' myth to the test. Four predict-test-explain experiments, a predict-the-numbers challenge and ten guided set-ups lead to the real cause: the tilt of Earth's axis.
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The Scale of the Solar System
A powers-of-ten journey in both directions. Start next to a person standing on Earth and zoom out through a house, Mount Everest, the whole Earth, the Moon's orbit, the Sun and the planets, the nearest stars, the Milky Way and galaxy clusters to the edge of the observable universe. Or zoom in through skin, a cell, DNA and a carbon atom to the quarks inside one proton. Nothing is squashed to fit: switch off the helper markers and the planets vanish into empty space. Live readouts give the field of view, how long light takes to cross it, the next object beyond the view and how much of the picture is actually “stuff”. Fire a beam of light at the Moon, the Sun or a star and time it, compare any two objects side by side, shrink Earth to a pea to see where everything else would sit, and work through ten guided experiments with mission questions.
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Plate Tectonics & Boundary Types
A live cross-section through Earth's crust and upper mantle, with one plate on each side of a boundary. Make each plate oceanic or continental and send it toward the boundary, away from it or sliding past it, then fast-forward millions of years. Continents crumple into mountains with deep roots, oceanic plates dive under to make trenches and volcanic arcs, continents split into rift valleys, ridges spread new sea floor with magnetic stripes, and transform faults lock and slip. Every earthquake is logged with its depth and magnitude on a seismograph and a depth map, a map view shows the plates from above, and each boundary comes with a real place on Earth. Predict before you play, match ten famous places to their boundary types, and work through ten guided experiments.
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Water Cycle & Watershed Lab
A working model of a watershed, the land that drains into one river. Set the rain, sunshine, slope, land cover, soil type and starting wetness, add a dam or storm drains, and watch the water move hour by hour in an animated side view: caught by leaves, soaking into the soil, seeping down to groundwater, running over the land into the river and evaporating back into the sky. A live storm hydrograph marks the peak flow and lag time, water-store tanks and flood and drought warnings show what the river is doing, a stores-and-flows diagram shows the whole water cycle as a system, and a bird's-eye map shows how tributaries gather into one outlet. Pin any run as a comparison, try five guided experiments and work through ten fair tests.
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The Coriolis Playground
Three linked labs about the Coriolis effect. In the Parcel launcher you fire puffs of air across a 3-D globe, set Earth's spin speed (even stop or reverse it), the release latitude and longitude, launch direction and speed, then flip between the view from space and the view from the spinning ground to discover that the parcel really flies straight while the ground turns beneath it. Predict which way each parcel will turn, release twin parcels in both hemispheres and read the deflection in kilometres. The Global wind belts map shows how the same sideways bending turns flow between pressure belts into the trade winds, westerlies and polar easterlies, with a side view of the Hadley, Ferrel and Polar cells. The Cyclone maker shows air rushing into a low-pressure centre being swirled into a storm that spins anticlockwise in the north and clockwise in the south. Ten guided experiments set everything up for you.
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Sleep Debt Lab
A week-long sleep planner built on the scientific two-process model. Drag bedtimes, wake-ups, naps and coffees on a sleep diary (or edit them in a schedule table), set your sleep need and caffeine half-life, add morning sunlight or late-night screens, and fly east or west across time zones. The model works out, every five minutes, your sleep pressure (Process S), your body clock (Process C), caffeine level and running sleep debt, and from them your alertness. Hover any chart or play the week to watch the readouts change, read the sleep coach's notes, try twelve ready-made weeks (6-hour nights, weekend lie-ins, late coffee, power naps, jet lag, night shifts, an all-nighter) and work through ten experiments.
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Heart Zone Trainer
Build a training plan for a virtual athlete and play it out day by day. Set age, resting heart rate and starting fitness to get maximum heart rate and the four heart-rate zones in beats per minute, then mark each weekday as rest, easy or hard and choose intensity (% of max HR), session length, number of weeks and recovery weeks. A live monitor sweeps each session's heart-rate trace through the zones with oxygen use, the talk test and a beating heart, while four charts fill in: fitness vs fatigue (Banister's impulse-response model and TRIMP training load), daily body rebuilding, VO₂ max and resting heart rate, and an overtraining meter. Compare two athletes or two plans side by side, read the coach's verdict, and work through ten experiments, from max-zone-every-day to a coach challenge.
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Drug Dosing & Half-Life Lab
A one-compartment pharmacokinetic model with first-order absorption (the Bateman equation), summed over every dose. Pick an example drug or build your own: set the dose, dosing interval, loading dose, half-life, absorption speed (tablet to IV), volume of distribution and the therapeutic window. Press play to watch the blood level build up dose by dose towards steady state while purple drug dots travel from the gut into the blood and out through the liver and kidneys. Skip or add doses, scrub the clock, pin a curve to compare before and after, and read live numbers: steady-state peak and trough, accumulation factor, elimination rate, time to steady state and time in the safe window. Six guided experiments and ten more to try cover half-lives, accumulation, loading doses, missed doses and a narrow-window challenge.
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Hydration & Electrolyte Balance
A body-fluid model of a runner exercising in the heat. Every simulated minute it adds and removes water and sodium through drinks, salty food, sweat, urine and breathing, then works out blood sodium (salt ÷ water), osmolality, ADH, thirst and urine output. Set body mass, temperature, race length, sweat rate and sweat saltiness, then choose how much to drink, what to drink (plain water, sports drink or ORS) and how much salt to eat, or let the runner drink to thirst. Watch the runner, the body-water tank, a swelling or shrinking brain cell and the kidneys respond; follow sodium and body mass on live charts; compare all three drinks at once; and read the water and sodium balance sheet. Six guided experiments, a marathon challenge and ten more experiments cover dehydration, hyponatraemia, electrolytes, kidneys and planning intake.
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Carbon Budget & Tipping Points
Design a global CO₂ pathway with sliders for growth, peak year, rate of decline and net-zero year, or drag the decade dots to draw your own curve. Add carbon removal, pick a target temperature and switch on tipping-point feedbacks. The model adds up emissions year by year, turns the running total into warming with the TCRE rule, tracks atmospheric CO₂ with a one-box carbon cycle and checks warming against nine climate tipping elements. Press play to watch the decades go by: four live charts, budget bars for your target, 1.5 °C and 2 °C, a years-left clock, a tipping-point tracker and a milestone timeline. Pin a pathway to compare before and after. Six guided experiments and ten more to try cover flat emissions, deep cuts, delay, carbon removal, net-zero timing, feedbacks and overshoot.
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The Shared Lake: Tragedy of the Commons
A shared-fishery game built on logistic (Schaefer) surplus production with an Allee effect. Each season you choose your catch while computer fishers with greedy, fair, cautious and copycat personalities choose theirs; the fish are sold for $10 each and the survivors breed. Change the number of fishers, the regrowth rate, the game length and the rules: open access, a per-fisher quota, private property zones, or a talk round where a deal is only as strong as the group's trust. Watch the animated lake, the fish-stock chart, a catch-versus-regrowth sustainability gauge, the money table and a season report that shows what would happen if everyone fished like you. Five guided experiments and ten more to try cover greed, collapse, quotas, cooperation, time horizons, breeding rates, crowding, property rights and the maximum sustainable yield.
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