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Each cell has an x and y coordinate, just like a pixel.\",instruction:\"Click a cell to inspect its coordinates.\",code:\"const field = createScalarField(28, 18);\\n\\nfield.at(x, y);\",notice:\"A two-dimensional cell can live in a one-dimensional array.\",notYet:\"There is no stored fluid quantity and no motion yet.\"},\n scalar:{number:\"section 2\",title:\"One number in every cell\",text:\"A scalar field stores one value at each location. Here the value represents an abstract amount of blue dye.\",instruction:\"Click and drag to paint dye into cells.\",code:\"field.set(x, y, dyeAmount);\\n\\nrenderScalarField(field);\",notice:\"Color is only a picture of the numbers. The Float32Array is the model.\",notYet:\"The dye does not move or spread by itself.\"},\n diffusion:{number:\"section 3\",title:\"State changes in steps\",text:\"A simulation repeatedly derives a new field from the current field. The slider controls how far each cell moves toward its neighbor average during the next step.\",instruction:\"For a fair comparison: choose a percentage, press example, then press step.\",code:\"while (running) {\\n field = diffuseScalarField(field);\\n renderScalarField(field);\\n}\",notice:\"The slider affects future steps; it cannot recalculate steps already taken. Compare 5% and 100% from the same example state.\",notYet:\"This is diffusion only—not velocity, advection, pressure, or a complete fluid solver.\"},\n velocity:{number:\"checkpoint 2\",title:\"Two numbers in every cell\",text:\"A velocity field stores a horizontal component vx and a vertical component vy at each location. An arrow visualizes that pair.\",instruction:\"Drag from one cell toward another to assign a direction, or press example.\",code:\"velocity.set(x, y, { vx, vy });\\n\\nrenderVectorField(velocity);\",notice:\"Arrow direction shows the vector direction. Arrow length represents its magnitude.\",notYet:\"The arrows describe possible motion, but nothing follows them yet. Transport comes next with advection.\"},\n advection:{number:\"checkpoint 3\",title:\"Use velocity to transport dye\",text:\"Advection connects the fields. For every destination cell, we trace backward along its velocity and sample the dye value found there.\",instruction:\"Press example, then advance the dye one step at a time.\",code:\"dye = advectScalarField(\\n dye,\\n velocity\\n);\\n\\nrenderScalarField(dye);\",notice:\"The velocity field is not the dye. It tells the update where each new dye value should come from.\",notYet:\"This uses semi-Lagrangian sampling. It is stable and visual, but it can blur dye and does not conserve its total amount exactly.\"},\n transportDiffusion:{number:\"checkpoint 4\",title:\"Transport, then spread\",text:\"A fluid step can apply multiple updates in sequence. First advection transports the dye. Then diffusion exchanges dye with neighboring cells.\",instruction:\"Press example, choose both strengths, and advance one combined step at a time.\",code:\"dye = advect(dye, velocity);\\ndye = diffuse(dye, diffusion);\\n\\nrenderScalarField(dye);\",notice:\"Advection changes where the pattern goes. Diffusion changes how sharp or spread-out the pattern is.\",notYet:\"This diffuses the dye quantity, not the velocity field. We also have not enforced incompressibility or solved pressure.\"},\n divergence:{number:\"checkpoint 5\",title:\"Where flow expands or compresses\",text:\"Divergence measures the net flow leaving each cell. Positive values behave like sources; negative values behave like sinks; values near zero have balanced inflow and outflow.\",instruction:\"Press example. Red cells are sources, blue cells are sinks. Click a cell to inspect its divergence.\",code:\"divergence = measureDivergence(velocity);\\n\\n// target for incompressible flow\\ndivergence ≈ 0;\",notice:\"A velocity field can look smooth while still creating or destroying volume. Divergence gives us a number that exposes that problem.\",notYet:\"We only measure the error here. The next lesson will solve pressure and subtract its gradient to reduce divergence.\"},\n projection:{number:\"checkpoint 6\",title:\"Use pressure to correct velocity\",text:\"Projection converts divergence into a pressure field, then subtracts the pressure gradient from velocity. The correction pushes away from compression and resists expansion.\",instruction:\"Press example, note the red and blue error, then press step to project the velocity.\",code:\"divergence = measureDivergence(velocity);\\npressure = solvePressure(divergence);\\nvelocity -= gradient(pressure);\",notice:\"Pressure is not painted manually. It is solved from the divergence error, used to correct velocity, and recalculated on the next step.\",notYet:\"The iterative pressure solve is approximate, and wall boundary conditions are still simplified. The next lesson will make boundaries explicit.\"},\n boundaries:{number:\"checkpoint 7\",title:\"Fluid cannot cross a solid wall\",text:\"A wall removes the velocity component pointing through it. Motion parallel to the wall can remain, so the fluid slides along the surface instead of escaping.\",instruction:\"Press example. Red wall cells leak outward; press step to enforce no-through boundaries.\",code:\"velocity = enforceNoThroughWalls(velocity);\\n\\nnormalVelocityAtWall = 0;\",notice:\"At left and right walls we remove horizontal velocity. At top and bottom walls we remove vertical velocity.\",notYet:\"This is a free-slip wall: tangential motion remains. We have not yet implemented no-slip friction, obstacles, or coupled projection at the boundary.\"},\n temperature:{number:\"checkpoint 8\",title:\"Heat creates upward acceleration\",text:\"Temperature is another scalar field. Hotter fluid is less dense, so buoyancy adds upward velocity where temperature is high.\",instruction:\"Press example, choose a buoyancy strength, then press step. Watch the arrows grow upward inside the hot region.\",code:\"velocity = applyBuoyancy(\\n velocity,\\n temperature\\n);\",notice:\"Temperature does not move anything directly. It changes velocity; velocity can move dye later through advection.\",notYet:\"Temperature does not diffuse or advect yet. We also omit ambient cooling, gravity calibration, density, and wax phase changes.\"},\n thermalFlow:{number:\"checkpoint 9\",title:\"The local-force gap\",text:\"Buoyancy changes velocity only where heat already exists. Backward advection in neighboring stationary cells cannot discover that heat, so a bottom row can remain pinned.\",instruction:\"Paint the bottom row and step. This deliberately preserves the gap you noticed.\",code:\"velocity = applyBuoyancy(velocity, temperature);\\ntemperature = advect(temperature, velocity);\",notice:\"Composing two correct operations is not enough if the velocity field has not been made into a coherent fluid-wide flow.\",notYet:\"This version skips pressure projection and boundary enforcement between force and transport. The next module inserts them.\"},\n coupledThermal:{number:\"checkpoint 10\",title:\"Spread the push before transport\",text:\"Pressure projection turns the local buoyant push into a divergence-reduced velocity field. Wall enforcement keeps that corrected flow inside before it transports temperature.\",instruction:\"Paint a hot bottom row or press example, then step. Compare its motion with Module 11.\",code:\"velocity = applyBuoyancy(velocity, temperature);\\nvelocity = project(velocity);\\nvelocity = enforceWalls(velocity);\\ntemperature = advect(temperature, velocity);\",notice:\"Projection does not move heat. It reshapes velocity so neighboring cells participate; advection then moves the temperature.\",notYet:\"The heater is not continuous and temperature does not diffuse or cool. Those processes come next.\"},\n heatedFlow:{number:\"checkpoint 11\",title:\"Temperature needs a source and a sink\",text:\"A real lamp keeps receiving energy from its bulb while losing energy to its surroundings. Each step adds heat near the bottom and removes a percentage everywhere.\",instruction:\"Press clear, then step repeatedly. Adjust heater and cooling to see whether heat accumulates or fades.\",code:\"temperature = cool(temperature);\\ntemperature = addBottomHeat(temperature);\\nvelocity = applyBuoyancyAndProject(velocity, temperature);\\ntemperature = advect(temperature, velocity);\",notice:\"The temperature field is no longer just initial data. It is driven over time by competing input and loss rates.\",notYet:\"Cooling is uniform rather than stronger at the glass, and heat does not diffuse by conduction. We still have only one material.\"},\n conductiveFlow:{number:\"checkpoint 12\",title:\"Heat also travels without bulk motion\",text:\"Conduction exchanges temperature between neighboring cells. The glass boundary then removes extra heat only from edge cells, creating a spatially meaningful heat sink.\",instruction:\"Press clear and step repeatedly. Compare low and high conduction, then change wall cooling.\",code:\"temperature = addBottomHeat(temperature);\\ntemperature = diffuseTemperature(temperature);\\ntemperature = coolAtWalls(temperature);\\nvelocity = solveFlow(velocity, temperature);\\ntemperature = advect(temperature, velocity);\",notice:\"Advection carries heat with moving fluid. Conduction spreads heat between neighbors even when the local velocity is zero.\",notYet:\"The walls all use one cooling rate and the heater has an abstract strength. We still have one continuous material rather than wax in a carrier liquid.\"},\n waxField:{number:\"checkpoint 13\",title:\"Material identity is another scalar field\",text:\"Wax fraction stores how much of each cell is wax: 0 is carrier liquid, 1 is wax, and values between represent a numerically mixed cell.\",instruction:\"Press example or paint wax, then step. Pink shows wax while the underlying warmth still affects the shared velocity.\",code:\"wax = advect(wax, velocity);\\ntemperature = advect(temperature, velocity);\",notice:\"Wax fraction and temperature coexist at every cell. Advection can transport both fields through the same velocity without confusing what they mean.\",notYet:\"Wax does not yet have different density or viscosity, and it does not melt or solidify. This is material tracking, not phase-change physics.\"},\n densityWax:{number:\"checkpoint 14\",title:\"Wax buoyancy depends on relative density\",text:\"Temperature changes wax density relative to the carrier. Wax hotter than neutral gets an upward force; colder wax gets a downward force.\",instruction:\"Press example: the left blob is hot and low, the right blob is cold and high. Step and compare their directions.\",code:\"densityError = wax * (neutralTemperature - temperature);\\nvelocity.y += densityError * response;\",notice:\"The force combines temperature and material identity. Equally hot carrier liquid does not receive this wax-specific density force.\",notYet:\"Values are normalized rather than kg/m³, and the relationship is linear. Wax still has no temperature-dependent viscosity or solid state.\"},\n phaseWax:{number:\"checkpoint 15\",title:\"Temperature changes how freely wax moves\",text:\"Wax identity remains constant, but a smooth phase fraction is derived from temperature. Cold wax is mostly solid and damps local velocity; hot wax is mostly liquid and follows the flow.\",instruction:\"Press example, then step. Watch the initially cold wax resist motion until heating moves it through the melting range.\",code:\"liquid = smoothMelt(temperature, meltPoint, width);\\nvelocity *= 1 - wax * (1 - liquid) * solidDrag;\",notice:\"Material identity and phase state are different: wax remains wax while its liquid fraction changes continuously from 0 to 1.\",notYet:\"Solid drag is a teaching approximation, not a full viscosity or viscoelastic stress solve. Latent heat and surface tension are still absent.\"},\n interfaceWax:{number:\"checkpoint 16\",title:\"A wax boundary is made of fractional cells\",text:\"Bilinear advection creates cells containing partial wax. The renderer now respects that fraction, and an optional sharpening pass nudges mixed values toward 0 or 1.\",instruction:\"Press example and step. Compare 0% and 100% sharpening, and inspect the wax value at the edge.\",code:\"wax = advect(wax, velocity);\\nwax = sharpenInterface(wax, strength);\",notice:\"Faint edge cells are numerical mixtures, not fully solid wax. Wax fraction must affect both the simulation and its rendering.\",notYet:\"This smoothstep sharpening is not mass-conserving and is not a full VOF, level-set, or surface-tension method.\"},\n latentWax:{number:\"checkpoint 17\",title:\"Melting consumes energy\",text:\"Wax now stores melt progress separately from temperature. Near the melting point, added energy advances the phase instead of immediately making the wax hotter.\",instruction:\"Press example, select a wax cell, and step. Watch temperature linger near the melt point while melt progress rises.\",code:\"energy = exchangeLatentHeat(temperature, meltProgress);\\n// temperature plateaus while phase changes\",notice:\"A phase transition can store energy without a matching temperature increase. Solidifying releases that stored energy back into temperature.\",notYet:\"The latent capacity is normalized and approximate; we do not yet use joules, specific heat, or a fully conservative enthalpy formulation.\"},\n surfaceWax:{number:\"checkpoint 18\",title:\"The wax boundary creates a force\",text:\"A gradient estimates the interface normal. Changes in that normal estimate curvature. Surface tension applies a force proportional to curvature near the wax boundary.\",instruction:\"Press example and step. Compare surface tension at 0 and 1; cyan cells mark the mixed interface.\",code:\"normal = normalize(gradient(wax));\\ncurvature = -divergence(normal);\\nforce = surfaceTension * curvature * gradient(wax);\",notice:\"Surface tension acts at the interface, not throughout the wax. It resists highly curved, ragged boundaries and encourages coherent blobs.\",notYet:\"This coarse continuum-surface-force approximation can create numerical currents and is not quantitatively calibrated.\"},\n viscosityWax:{number:\"checkpoint 19\",title:\"Viscosity diffuses momentum\",text:\"Each cell moves its velocity toward the average of neighboring velocities. The blend strength depends on whether the cell is carrier, hot liquid wax, or cold wax.\",instruction:\"Press example and step. Compare low and high cold-wax viscosity, then inspect viscosity at hot and cold wax cells.\",code:\"viscosity = mixByMaterialAndPhase(carrier, hotWax, coldWax);\\nvelocity = diffuseVelocity(velocity, viscosity);\",notice:\"Diffusing dye spreads a scalar quantity. Viscosity uses similar neighbor exchange on velocity, smoothing differences in momentum.\",notYet:\"These are normalized per-step blend rates, not Pa·s. Variable-viscosity diffusion is approximate and solid drag remains a separate teaching force.\"},\n stableLamp:{number:\"checkpoint 20\",title:\"One frame can contain several smaller solves\",text:\"The complete physics order is fixed. A frame time is divided by the selected substep count, and rate-like updates are scaled by that smaller duration.\",instruction:\"Press example. Compare one substep with eight at the same time per frame, and watch maximum travel per substep.\",code:\"for (const dt of subdivide(frameTime)) {\\n addHeatAndCool(dt);\\n updatePhaseAndForces(dt);\\n diffuseAndProjectVelocity(dt);\\n enforceWalls();\\n advectFields(dt);\\n}\",notice:\"Substeps do not add new physics. They reduce how far information travels before fields are recomputed, improving numerical stability.\",notYet:\"This still uses normalized units and explicit approximations. The final lesson adds continuous time, playback controls, and lamp-oriented presets.\"},\n simulator:{number:\"checkpoint 21\",title:\"The complete lamp runs continuously\",text:\"A fixed-rate animation loop repeatedly executes the stable timestep. Presets choose coherent groups of parameters rather than changing one coefficient in isolation.\",instruction:\"Choose a preset, press example, then play. Pause at any time to inspect a cell or advance one frame manually.\",code:\"while (playing) {\\n accumulator += elapsedTime;\\n while (accumulator >= frameInterval)\\n stepCompleteLamp();\\n}\",notice:\"The simulator runtime does not add physics. It schedules the validated timestep repeatedly and exposes diagnostics that reveal drift or instability.\",notYet:\"Parameters remain normalized and visually calibrated. This is a complete educational browser simulator, not a quantitatively validated industrial multiphase CFD model.\"},\n unevenHeating:{number:\"checkpoint 22\",title:\"Perfect symmetry prevents separate blobs\",text:\"A broad wax pool now rests above a heater whose strength varies across space and slowly over time. Small thermal differences seed separate buoyant regions.\",instruction:\"Press example, compare unevenness at 0% and 100%, then play. Watch for localized hot spots instead of uniform lifting.\",code:\"localHeat = heater * (1 + spatialPerturbation);\\ntemperature.bottom += localHeat;\",notice:\"The perturbation does not create motion directly. It creates temperature differences that density and buoyancy amplify into different rising regions.\",notYet:\"Pinch-off and merging still depend on the coarse interface method. The next step focuses on necking, separation, and recombination.\"},\n pinchOff:{number:\"checkpoint 23\",title:\"Thin wax bridges can become separate blobs\",text:\"The coarse grid cannot resolve a neck thinner than one cell, so this lesson adds an explicit topology rule: detect a strained, partially filled bridge, remove wax from its neck, and return that wax to its thicker neighbors.\",instruction:\"Press example, then play. Cyan cells are neck candidates. Compare pinch strength at 0% and 100%, and watch separated blobs merge naturally when advection brings their interfaces together.\",code:\"neck = detectThinBridge(wax, velocity);\\nremoved = pinch(neck);\\nredistributeConservatively(removed);\",notice:\"Pinch-off is a change in connectivity. The algorithm severs only narrow, strained bridges and conserves the wax it moves. Recombination needs no opposite rule: overlapping interfaces already become one connected field.\",notYet:\"This is a transparent teaching approximation, not a resolved Rayleigh–Plateau instability. A finer adaptive grid or particle/interface method would produce breakup from the governing forces themselves.\"},\n conservation:{number:\"checkpoint 24\",title:\"Wax may move, but its total amount should not change\",text:\"Advection and interface sharpening operate cell by cell, so rounding and nonlinear sharpening can create or destroy wax numerically. This lesson records total wax before each substep and audits it afterward.\",instruction:\"Press example and play. Set mass correction to 0% to expose raw drift, then 100% and compare the two diagnostics.\",code:\"targetMass = sum(waxBefore);\\nrunPhysics();\\nerror = targetMass - sum(waxAfter);\\nredistribute(error, interfaceCells);\",notice:\"Conservation is a constraint on the whole field, not a property of one cell. Individual cell values may change while their sum remains constant.\",notYet:\"The correction preserves normalized wax volume, not physical mass derived from density and cell volume. Energy and momentum also deserve separate conservation audits.\"},\n energyBudget:{number:\"checkpoint 25\",title:\"Heat has sources, sinks, and storage\",text:\"Unlike wax volume, thermal energy is not expected to remain constant. The heater adds it, ambient and wall cooling remove it, and melting transfers it between temperature and latent storage.\",instruction:\"Press example and play. Change heater and cooling strength, then watch which ledger entries respond. Stored latent energy can rise even while temperature pauses.\",code:\"energy = sum(temperature + meltProgress);\\nchange = heaterInput + coolingLoss + numericalDrift;\",notice:\"A conservation law is an accounting identity: system change equals energy crossing the boundary plus numerical error. Constant energy is expected only in a closed system.\",notYet:\"The ledger uses normalized energy units and omits kinetic and gravitational potential energy. The next refinement would audit the complete mechanical-plus-thermal budget.\"},\n closedVessel:{number:\"checkpoint 26\",title:\"A closed lamp has a fixed material inventory\",text:\"Previously, painting set a cell to wax without removing wax anywhere else. Conservation then faithfully preserved that newly enlarged total. In this lesson, painting relocates wax from the existing field instead.\",instruction:\"Press example. Note the total wax, then click or drag through empty cells. Wax leaves other locations—starting with the bottom reservoir—as the selected cells fill.\",code:\"amount = withdraw(waxInventory);\\ntarget.wax += amount;\\n// carrier fraction is always 1 - wax fraction\",notice:\"Every cell is already full: wax fraction plus carrier-liquid fraction equals one. Adding wax to a cell means displacing carrier there and taking wax from somewhere else in the closed lamp.\",notYet:\"The relocation gesture is an educational editing constraint, not fluid motion. During play, advection and pressure remain responsible for physical transport.\"},\n cycleDiagnostics:{number:\"checkpoint 27\",title:\"A cycle is a pattern measured over time\",text:\"One frame cannot tell us whether wax is circulating. We track the wax-weighted center height and the fractions currently moving upward or downward, then retain a short history.\",instruction:\"Press example and play. Look for the height trace to rise and fall repeatedly. A flat trace means the lamp has approached a steady arrangement, even if local cells still move.\",code:\"height = weightedCenter(wax);\\nrising = sum(wax where velocity.y < 0);\\nfalling = sum(wax where velocity.y > 0);\",notice:\"Oscillation is a property of a sequence of states, not one state. Center of mass compresses the whole wax field into one useful—but incomplete—signal.\",notYet:\"The trace does not identify individual blobs. Object tracking would be needed to measure each blob’s lifetime, speed, split, and merge events.\"},\n particleVolume:{number:\"checkpoint 35\",title:\"Wax particles need pressure as well as cohesion\",text:\"A smoothing kernel estimates crowding. Density above the target creates outward pressure, preventing many particles from occupying one point.\",instruction:\"Press example and play. Raise volume pressure until wax spans several cells, then tune cohesion to keep that finite volume connected.\",code:\"density = kernelSum(neighbors);\\npressure = max(0, density - restDensity);\",notice:\"Pressure preserves particle volume; cohesion shapes it. Bilinear transfer couples each particle to four grid cells.\",notYet:\"This is an SPH-style teaching approximation, not an iterative PBF solve.\"},\n shapedLamp:{number:\"checkpoint 34\",title:\"The vessel shape completes the circulation path\",text:\"Wax is a configurable fixed particle mass moving through the projected carrier grid. Uneven heating creates internal density differences, while hot particles weaken their cohesion enough for a large cluster to neck and separate.\",instruction:\"Press example and play. Compare low and high base concentration. Watch fallen wax gather centrally, reheat locally, and launch again.\",code:\"inside = lampShape(cell);\\nheat = focusedBaseHeater(x);\\nenforceCurvedWalls(velocity);\",notice:\"More particles create a deformable wax body rather than a tiny point cluster. Cold particles cohere strongly at the base; unevenly heated particles rise at different rates and can pull the body apart.\",notYet:\"The particle-to-grid transfer is deliberately simple and the rendered surface is an overlap visualization rather than a calibrated SPH kernel.\"},\n finalLamp:{number:\"checkpoint 33\",title:\"The complete educational lava lamp\",text:\"The final mode runs one authoritative timestep: heat, cooling, phase exchange, buoyancy, surface force, viscosity, pressure projection, walls, transport, pinch-off, and conservation.\",instruction:\"Choose a preset, press example, then play. Use the compact diagnostics to judge whether wax is forming blobs and completing a rise-and-fall cycle.\",code:\"while (playing) stepLavaLamp();\",notice:\"The final picture is the consequence of interacting fields and constraints, not a scripted blob animation.\",notYet:\"This remains a coarse normalized teaching model, not a quantitatively validated industrial multiphase CFD solver.\"},\n physicalUnits:{number:\"checkpoint 32\",title:\"Normalized values need a scale to become units\",text:\"A velocity of one means one cell per simulation frame. Choose a cell width and frame duration to interpret that same value as centimeters per second.\",instruction:\"Play, then change cell width and seconds per frame. The motion is unchanged; only its physical interpretation changes.\",code:\"speedCmPerSecond = velocityCellsPerFrame * cellWidthCm / secondsPerFrame;\",notice:\"Units do not appear automatically. A nondimensional simulation becomes physical only after selecting reference scales.\",notYet:\"The coefficients are visually calibrated and cannot yet be claimed as measured wax viscosity, density, or surface tension.\"},\n calibration:{number:\"checkpoint 31\",title:\"A lamp is calibrated as a system\",text:\"Heating, cooling, viscosity, density response, and surface tension must produce a bounded repeating cycle together. No single best slider value exists in isolation.\",instruction:\"Compare the balanced, slow, and active presets. Watch height range and blob count instead of judging only instantaneous speed.\",code:\"preset = calibrateTogether({heat,cooling,viscosity,density,surface});\",notice:\"Calibration chooses a useful regime of behavior; it does not add new governing physics.\",notYet:\"These presets are visual targets rather than fits to measurements from a specific manufactured lamp.\"},\n motionMatch:{number:\"checkpoint 30\",title:\"Identity matching needs motion tolerance\",text:\"A fast blob may move into entirely new cells between frames. When direct overlap fails, the tracker searches nearby previous cells before declaring a new identity.\",instruction:\"Play and compare a search radius of zero with one or two cells. Larger radii preserve identity through faster motion but can confuse nearby blobs.\",code:\"match = overlap || nearbyPreviousIdentity(searchRadius);\",notice:\"Tracking is an inference problem layered over the simulation. Greater tolerance reduces lost identities but increases ambiguous matches.\",notYet:\"The matcher expands spatially rather than predicting a velocity-directed future centroid.\"},\n blobIdentity:{number:\"checkpoint 29\",title:\"Identity comes from overlap across frames\",text:\"Each connected region compares its cells with the previous frame. The strongest overlap inherits the old identity; unmatched regions receive a new one.\",instruction:\"Press example and play. Outline colors now persist as blobs travel. Splits share a parent identity and merges overlap multiple previous identities.\",code:\"identity = largestOverlap(currentBlob, previousBlobs);\\nif (!identity) identity = nextId++;\",notice:\"Connectivity answers what is one blob now. Temporal matching answers whether it is the same blob as before.\",notYet:\"Fast motion can defeat pure overlap matching. A production tracker would also compare centroid, volume, and velocity.\"},\n blobTracking:{number:\"checkpoint 28\",title:\"A blob is a connected region, not a special particle\",text:\"We threshold the wax fraction, then flood-fill neighboring wax cells. Every connected component receives a label, size, and colored outline.\",instruction:\"Press example and play. Change the connection threshold and watch weak fractional bridges either join regions or separate them. Split and merge counts respond when the component count changes.\",code:\"mask = wax > threshold;\\nblobs = connectedComponents(mask, fourNeighbors);\",notice:\"Blob identity is derived from the wax field. The simulation never stores a blob object; connected shapes emerge from neighboring cell values.\",notYet:\"A changing component count is only an apparent split or merge. Robust event tracking must match component overlap across frames so threshold flicker is not mistaken for topology change.\"}\n };\n\n","createdAt",["D",1785333842238],"branchVersion","branchId","821943c5-8c6e-4b33-9dd7-51e1353405e8","id","6fa4f715-b236-46ca-b183-2820945d7d51","laval",["D",1784854669144],"deletedAt","legacyEnvVars",false,"privacy","public","httpPrivacy","description","Learn fluid simulation through a lava lamp.","imageUrl","40e69d1a-3254-4858-920b-7b1449761575","pinnedFileId","b0d26520-86fa-11f1-9ca8-1607ee4eb77e","pinPreview","pinMigrated","screenshotVersion","likeCount",0,"orgId","54bae3d1-8223-41e5-b22d-81eb28a263c7","tursoName","tursoHostname","tursoMeasuredAt","pinned","userPerm","r","valPerm","blobPerm","rw","emailPerm","sqlitePerm","projectPerm","telemetryPerm","user",{"_97":96,"_104":100},"org",{"_97":96,"_98":-5,"_99":100,"_18":56,"_101":102,"_103":49},"branch",{"_13":86,"_32":87,"_43":42,"_88":44,"_89":-5,"_90":-5,"_91":-5,"_92":-5,"_93":-5,"_94":45,"_95":96},"isOwned",291,"main","projectId","forkedBranchId","forkedBranchVersion","forkedProjectPrivacy","forkedProjectId","forkedProjectOrgId","projectName","userHandle","pchinjr","handle","displayName","avatar","https://images.clerk.dev/oauth_github/img_2OaSpooJk6yZ5KFqyjtIVA4z3SH.jpeg","tier","free","canRestrictVals","profileImageUrl","branchName","","adoptOrgId",{"_43":44,"_32":45,"_38":341,"_47":-5,"_48":49,"_50":51,"_52":51,"_53":54,"_55":-5,"_18":56,"_57":58,"_59":25,"_60":-5,"_61":-5,"_62":63,"_64":65,"_66":-5,"_67":-5,"_68":-5,"_69":-5,"_70":71,"_72":71,"_73":74,"_75":74,"_76":74,"_77":71,"_78":71,"_79":342,"_81":343,"_83":344,"_85":49},"tree",[167,186,187],"files",[167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187],"counts",{"_156":63,"_157":158,"_159":63,"_160":161,"_162":163},"contents",[127,128,129],"upstreamProject","upstreamBranch","emptyEnvVars","flags",[],"hasHttpFiles","grants","orgs","customDomains",{},{"_43":149,"_32":150,"_30":151,"_132":-5,"_41":42,"_40":152,"_134":25,"_38":153,"_13":63,"_34":154,"_36":-5,"_24":49,"_139":-5,"_27":155},{"_43":141,"_32":142,"_30":143,"_132":-5,"_41":42,"_40":144,"_134":25,"_38":145,"_13":146,"_34":20,"_36":147,"_24":49,"_139":-5,"_27":148},{"_43":130,"_32":131,"_30":58,"_132":-5,"_41":42,"_40":133,"_134":25,"_38":135,"_13":136,"_34":137,"_36":138,"_24":49,"_139":45,"_27":140},"c81208e2-cbe0-40c9-9d9e-48d5d170c77d","main.ts","parentId",258,"latest",["D",1785252584636],145,"http","import { documentHtml } from \"./src/ui/document.ts\";\nimport { styles } from \"./src/ui/styles.ts\";\n\nconst headers = {\n html: { \"content-type\": \"text/html; charset=utf-8\" },\n css: { \"content-type\": \"text/css; charset=utf-8\" },\n};\n\nexport default function (request: Request) {\n const pathname = new URL(request.url).pathname;\n\n if (pathname === \"/styles.css\") {\n return new Response(styles, { headers: headers.css });\n }\n\n return new Response(documentHtml, { headers: headers.html });\n}\n","label",[131],"6edce35b-3a56-4d22-abb1-948507aa2da7","README.md","d9aa0084-86fa-11f1-87e4-1607ee4eb77e",287,["D",1785333832243],46,"# laval\n\nA readable, browser-based lava lamp simulation for learning how a small computational fluid model is assembled.\n\nLive simulator: https://laval.val.run/\n\n## Start here\n\nOpen `src/simulation/step.js`. It contains the complete authoritative frame:\n\n```js\nexport function stepLavaLamp(state, settings) {\n const deltaTime = settings.timeStep / settings.substeps;\n\n for (let substep = 0; substep < settings.substeps; substep++) {\n updateParticleTemperatures(state, settings, deltaTime);\n applyParticleVolumePressure(state, settings, deltaTime);\n applyParticleForces(state, settings, deltaTime);\n projectParticleMotion(state, settings);\n moveParticles(state, deltaTime);\n rasterizeParticles(state);\n }\n\n return measureSimulation(state);\n}\n```\n\nEvery operation accepts ordinary simulation data. Physics modules do not read sliders, draw the canvas, change buttons, or know which UI is running them.\n\n## Rebuild order\n\n1. `config.js` — choose a grid width, height, and cell size.\n2. `grid.js` — map two-dimensional coordinates to flat arrays.\n3. `settings.js` — define plain numerical model parameters.\n4. `state.js` — create particles and the grid fields.\n5. `geometry.js` — define the tapered vessel and particle collisions.\n6. `temperature.js` — heat particles at the bottom and cool them elsewhere.\n7. `particles.js` — add buoyancy, cohesion, volume pressure, motion, and rasterization.\n8. `projection.js` — deposit particle velocity to the grid, reduce divergence, and sample it back.\n9. `diagnostics.js` — measure the result without changing it.\n10. `step.js` — compose those operations into one frame.\n11. `renderer.js` and `app.js` — connect the core to a canvas and controls.\n\n## Architecture\n\n```text\nsrc/\n browser/\n app.js thin DOM and animation controller\n renderer.js canvas output\n config.js grid dimensions\n grid.js coordinate helpers\n\n simulation/\n settings.js\n state.js\n geometry.js\n temperature.js\n particles.js\n projection.js\n diagnostics.js\n step.js\n\n ui/\n document.ts\n styles.ts\n\n contracts.ts TypeScript description of the model\n```\n\n## State versus settings\n\n`state` contains values that evolve: particle positions, velocities, temperatures, grid velocity, pressure, and time.\n\n`settings` contains inputs selected before or during a run: heater strength, cooling, cohesion, pressure strength, target density, and timestep controls.\n\nThe UI changes `settings`. The simulation changes `state`.\n\n## What the model represents\n\nWax is a fixed collection of particles. Each particle stores position, velocity, and normalized temperature. Heating changes buoyancy. Pairwise cohesion attracts nearby particles. Neighbor-density pressure prevents them from collapsing into one point.\n\nParticle velocity is deposited bilinearly onto an Eulerian grid. Pressure projection reduces divergence on that grid, then the corrected velocity is sampled back to the particles. Analytic collisions keep particles inside the tapered vessel.\n\nThe model is deterministic and educational. Its normalized coefficients are not calibrated material constants, and its pressure calculation is an SPH-style teaching approximation rather than a production CFD solver.\n",[142],"ec02ba1f-9c0f-4799-880e-882f8edb6681","src","c305d0ec-86fa-11f1-ace5-1607ee4eb77e",2,["D",1784854699691],"directory",[150],"pulls","branches",1,"forks","envVars",{"_164":63,"_166":63},"connections",{"_164":63,"_165":63},"count","unfilledCount","emptyCount",{"_43":149,"_32":150,"_30":151,"_132":-5,"_41":42,"_40":152,"_134":25,"_38":338,"_13":63,"_34":154,"_36":-5,"_24":49,"_139":-5,"_189":339,"_27":340},{"_43":333,"_32":307,"_30":301,"_132":151,"_41":42,"_40":334,"_134":25,"_38":335,"_13":63,"_34":154,"_36":-5,"_24":49,"_139":-5,"_189":336,"_27":337},{"_43":324,"_32":325,"_30":326,"_132":301,"_41":42,"_40":327,"_134":25,"_38":328,"_13":329,"_34":35,"_36":330,"_24":49,"_139":-5,"_189":331,"_27":332},{"_43":316,"_32":317,"_30":318,"_132":301,"_41":42,"_40":319,"_134":25,"_38":320,"_13":63,"_34":35,"_36":321,"_24":49,"_139":-5,"_189":322,"_27":323},{"_43":308,"_32":309,"_30":310,"_132":301,"_41":42,"_40":311,"_134":25,"_38":312,"_13":63,"_34":35,"_36":313,"_24":49,"_139":-5,"_189":314,"_27":315},{"_43":298,"_32":299,"_30":300,"_132":301,"_41":42,"_40":302,"_134":25,"_38":303,"_13":63,"_34":35,"_36":304,"_24":49,"_139":-5,"_189":305,"_27":306},{"_43":293,"_32":236,"_30":230,"_132":151,"_41":42,"_40":294,"_134":25,"_38":295,"_13":63,"_34":154,"_36":-5,"_24":49,"_139":-5,"_189":296,"_27":297},{"_43":285,"_32":286,"_30":287,"_132":230,"_41":42,"_40":288,"_134":25,"_38":289,"_13":63,"_34":35,"_36":290,"_24":49,"_139":-5,"_189":291,"_27":292},{"_43":277,"_32":278,"_30":279,"_132":230,"_41":42,"_40":280,"_134":25,"_38":281,"_13":63,"_34":35,"_36":282,"_24":49,"_139":-5,"_189":283,"_27":284},{"_43":269,"_32":270,"_30":271,"_132":230,"_41":42,"_40":272,"_134":25,"_38":273,"_13":63,"_34":35,"_36":274,"_24":49,"_139":-5,"_189":275,"_27":276},{"_43":261,"_32":262,"_30":263,"_132":230,"_41":42,"_40":264,"_134":25,"_38":265,"_13":63,"_34":35,"_36":266,"_24":49,"_139":-5,"_189":267,"_27":268},{"_43":253,"_32":254,"_30":255,"_132":230,"_41":42,"_40":256,"_134":25,"_38":257,"_13":63,"_34":35,"_36":258,"_24":49,"_139":-5,"_189":259,"_27":260},{"_43":245,"_32":246,"_30":247,"_132":230,"_41":42,"_40":248,"_134":25,"_38":249,"_13":63,"_34":35,"_36":250,"_24":49,"_139":-5,"_189":251,"_27":252},{"_43":237,"_32":238,"_30":239,"_132":230,"_41":42,"_40":240,"_134":25,"_38":241,"_13":63,"_34":35,"_36":242,"_24":49,"_139":-5,"_189":243,"_27":244},{"_43":227,"_32":228,"_30":229,"_132":230,"_41":42,"_40":231,"_134":25,"_38":232,"_13":63,"_34":35,"_36":233,"_24":49,"_139":-5,"_189":234,"_27":235},{"_43":222,"_32":213,"_30":207,"_132":151,"_41":42,"_40":223,"_134":25,"_38":224,"_13":63,"_34":154,"_36":-5,"_24":49,"_139":-5,"_189":225,"_27":226},{"_43":214,"_32":215,"_30":216,"_132":207,"_41":42,"_40":217,"_134":49,"_38":218,"_13":152,"_34":35,"_36":219,"_24":49,"_139":-5,"_189":220,"_27":221},{"_43":204,"_32":205,"_30":206,"_132":207,"_41":42,"_40":208,"_134":49,"_38":209,"_13":158,"_34":35,"_36":210,"_24":49,"_139":-5,"_189":211,"_27":212},{"_43":195,"_32":196,"_30":197,"_132":151,"_41":42,"_40":198,"_134":25,"_38":199,"_13":200,"_34":35,"_36":201,"_24":49,"_139":-5,"_189":202,"_27":203},{"_43":141,"_32":142,"_30":143,"_132":-5,"_41":42,"_40":144,"_134":25,"_38":192,"_13":146,"_34":20,"_36":147,"_24":49,"_139":-5,"_189":193,"_27":194},{"_43":130,"_32":131,"_30":58,"_132":-5,"_41":42,"_40":133,"_134":25,"_38":188,"_13":136,"_34":137,"_36":138,"_24":49,"_139":45,"_189":190,"_27":191},["D",1785252584636],"children",[],[131],["D",1785333832243],[],[142],"208ae2da-7562-4a89-8aaa-7a04306939e5","contracts.ts","db9d981a-86fa-11f1-aed7-1607ee4eb77e",286,["D",1785333828580],41,"export interface WaxParticle {\n x: number;\n y: number;\n vx: number;\n vy: number;\n temperature: number;\n}\n\nexport interface SimulationSettings {\n particleCount: number;\n heaterStrength: number;\n coolingRate: number;\n glassCoolingRate: number;\n heaterFocus: number;\n neutralTemperature: number;\n densityResponse: number;\n particleCohesion: number;\n restDensity: number;\n volumePressure: number;\n pressureIterations: number;\n timeStep: number;\n substeps: number;\n playbackRate: number;\n}\n\nexport interface SimulationDiagnostics {\n tick: number;\n particleCount: number;\n averageTemperature: number;\n waxHeight: number;\n maximumSpeed: number;\n maximumDensity: number;\n}\n\nexport interface SimulationState {\n particles: WaxParticle[];\n wax: Float32Array;\n temperature: Float32Array;\n velocityX: Float32Array;\n velocityY: Float32Array;\n divergence: Float32Array;\n pressure: Float32Array;\n pressureNext: Float32Array;\n vesselMask: Uint8Array;\n tick: number;\n time: number;\n diagnostics: SimulationDiagnostics | Record;\n indexOf(x: number, y: number): number;\n}\n",[],[150,196],"da1ea26b-916b-49d9-9713-d92182a7fd0e","styles.ts","4cb17186-8a96-11f1-a9d3-1607ee4eb77e","34766f7c-8a96-11f1-8334-1607ee4eb77e",284,["D",1785333679843],"export const styles = \":root{color-scheme:dark;--bg:#0d0f12;--panel:#15181d;--line:#303640;--text:#edf0f4;--muted:#929aa6;--blue:#50a7ff;--yellow:#ffd166}\\n*{box-sizing:border-box}\\nbody{margin:0;background:var(--bg);color:var(--text);font:14px/1.5 ui-monospace,SFMono-Regular,Menlo,monospace}\\n.shell{width:min(1120px,calc(100% - 28px));margin:auto;padding:34px 0 60px}\\nheader{display:flex;justify-content:space-between;gap:32px;align-items:end;margin-bottom:22px}\\nheader p{max-width:570px;color:var(--muted);margin:0}\\nh1{margin:0;font:750 52px/.9 system-ui,sans-serif;letter-spacing:-.06em}h1 span{color:var(--blue)}\\nh2{font:700 18px system-ui,sans-serif;margin:0 0 8px}\\ncode{color:#a8d5ff}.eyebrow{color:var(--yellow);text-transform:uppercase;letter-spacing:.13em;font-size:11px;margin-bottom:7px}\\n.workspace{display:grid;grid-template-columns:minmax(0,1fr) 300px;gap:16px;align-items:start}\\n.card{background:var(--panel);border:1px solid var(--line);border-radius:14px;overflow:hidden}\\n.canvas-head{display:flex;justify-content:space-between;align-items:center;gap:15px;padding:13px 15px;border-bottom:1px solid var(--line)}\\n.canvas-head b,.canvas-head span{display:block}.canvas-head span{color:var(--muted);font-size:11px;margin-top:2px}\\n.actions{display:flex;gap:7px}button{font:inherit;border:1px solid #414955;color:var(--text);background:#242a32;border-radius:7px;padding:7px 11px;cursor:pointer}\\nbutton.primary{background:var(--blue);border-color:var(--blue);color:#07111b;font-weight:700}\\n.canvas-wrap{padding:14px}canvas{display:block;width:100%;aspect-ratio:14/9;background:#090d13;border:1px solid #343b45}\\n.metrics{display:grid;grid-template-columns:repeat(6,1fr);border-top:1px solid var(--line)}\\n.metrics div{padding:10px;border-right:1px solid var(--line)}.metrics div:last-child{border:0}\\n.metrics b,.metrics small{display:block}.metrics b{color:var(--yellow)}.metrics small{color:var(--muted);font-size:9px;text-transform:uppercase}\\n.controls{padding:18px}.controls p{color:var(--muted);margin:0 0 18px}.controls label{display:block;margin:0 0 15px;font-size:12px}.controls output{float:right;color:var(--blue)}\\ninput[type=range]{display:block;width:100%;margin-top:6px;accent-color:var(--blue)}\\n.code-map{margin-top:16px;padding:20px;display:grid;grid-template-columns:1fr 1fr;gap:28px}\\n.code-map ol{margin:13px 0 0;padding-left:21px}.code-map li{margin:7px 0;color:var(--muted)}a{color:var(--blue)}\\npre{margin:0;background:#0d1117;border:1px solid #2b323b;border-radius:10px;padding:17px;overflow:auto;align-self:start}\\n@media(max-width:820px){header{align-items:start;flex-direction:column}.workspace,.code-map{grid-template-columns:1fr}.metrics{grid-template-columns:repeat(3,1fr)}}\\n\";\n",[],[150,213,205],"ui","748fadaa-abfb-4d51-b1b7-3a6ba9ca0bc1","document.ts","52b29326-8a96-11f1-bb6b-1607ee4eb77e",283,["D",1785333675542],"export const documentHtml = \"\\n\\n\\n \\n \\n laval — readable lava lamp simulation\\n \\n\\n\\n

\\n

one simulation · one readable timestep

\\n

laval

\\n

The lessons are now collapsed into the final model. Start with step.js, then follow each imported operation into the physics.

\\n

\\n\\n

\\n

\\n Hybrid particle lava lamp\\n temperature → pressure → forces → projection → motion\\n

\\n

\\n \\n \\n \\n

\\n

0frames

\\n

0particles

\\n

0average heat

\\n

0%wax height

\\n

0maximum speed

\\n

0maximum density

\\n

\\n\\n \\n

\\n\\n

\\n

reading order

\\n

Rebuild it in this order

\\n

step.js — the complete frame, readable top to bottom
state.js — authoritative particles and grid fields
temperature.js — heater and cooling
particles.js — buoyancy, cohesion, pressure and motion
projection.js — particle/grid velocity coupling
geometry.js — lamp shape and collisions
diagnostics.js — measurements only

\\n

stepLavaLamp(state, settings)\\n  updateParticleTemperatures()\\n  applyParticleVolumePressure()\\n  applyParticleForces()\\n  projectParticleMotion()\\n  moveParticles()\\n  rasterizeParticles()\\n  measureSimulation()

\\n

\\n\\n\\n\";\n",[],[150,213,215],"f1340c10-1007-45af-9382-df0fe0c3c541",230,["D",1785251315458],[183,184],[150,213],"455563c6-0b2f-4ddc-8247-2f61d2a7e1e6","temperature.js","91c24bf0-8b55-11f1-864d-1607ee4eb77e","747a0682-8b55-11f1-8efb-1607ee4eb77e",276,["D",1785333505864],"import { HEIGHT, WIDTH } from \"../browser/config.js\";\nimport { lampHalfWidth } from \"./geometry.js\";\n\nexport function updateParticleTemperatures(state, settings, deltaTime) {\n const center = (WIDTH - 1) / 2;\n const heaterWidth = 4 - 3 * settings.heaterFocus;\n const movingHotspot = 1.8 * Math.sin(state.tick * 0.045);\n\n for (let n = 0; n < state.particles.length; n++) {\n const particle = state.particles[n];\n const normalizedDistance = (particle.x - (center + movingHotspot)) / heaterWidth;\n const unevenness = 0.65 + 0.45 * (0.5 + 0.5 * Math.sin(particle.x * 2.1 + n * 0.17));\n\n if (particle.y > HEIGHT - 5.5) {\n particle.temperature +=\n settings.heaterStrength *\n deltaTime *\n Math.exp(-normalizedDistance * normalizedDistance) *\n unevenness;\n }\n\n particle.temperature *= 1 - settings.coolingRate * deltaTime;\n\n const wallGap = lampHalfWidth(particle.y) - Math.abs(particle.x - center);\n if (particle.y < 4 || wallGap < 1.2) {\n particle.temperature *= 1 - settings.glassCoolingRate * deltaTime;\n }\n\n particle.temperature = Math.max(0, Math.min(1, particle.temperature));\n }\n}\n",[],[150,236,228],"simulation","038e7c26-97c9-49c5-b89b-d6c003072a35","step.js","be109ad6-8b55-11f1-8b5e-1607ee4eb77e",280,["D",1785333580230],"import { measureSimulation } from \"./diagnostics.js\";\nimport {\n applyParticleForces,\n applyParticleVolumePressure,\n moveParticles,\n rasterizeParticles,\n} from \"./particles.js\";\nimport { projectParticleMotion } from \"./projection.js\";\nimport { updateParticleTemperatures } from \"./temperature.js\";\n\nexport function stepLavaLamp(state, settings) {\n const deltaTime = settings.timeStep / settings.substeps;\n let maximumDensity = 0;\n\n for (let substep = 0; substep < settings.substeps; substep++) {\n updateParticleTemperatures(state, settings, deltaTime);\n maximumDensity = applyParticleVolumePressure(state, settings, deltaTime);\n applyParticleForces(state, settings, deltaTime);\n projectParticleMotion(state, settings);\n moveParticles(state, deltaTime);\n rasterizeParticles(state);\n }\n\n state.tick++;\n state.time += settings.timeStep;\n state.diagnostics = measureSimulation(state, maximumDensity);\n return state.diagnostics;\n}\n",[],[150,236,238],"128ec34c-61c8-4b69-a4e1-582b0af09489","state.js","8f57c610-8b55-11f1-aa55-1607ee4eb77e",275,["D",1785333501824],"import { HEIGHT, WIDTH } from \"../browser/config.js\";\nimport { createGrid } from \"../browser/grid.js\";\nimport { buildLampMask, lampHalfWidth } from \"./geometry.js\";\n\nexport function createSimulationState(settings) {\n const cellCount = WIDTH * HEIGHT;\n const wax = new Float32Array(cellCount);\n const temperature = new Float32Array(cellCount);\n const grid = createGrid(WIDTH, HEIGHT, wax);\n\n const state = {\n particles: [],\n wax,\n temperature,\n velocityX: new Float32Array(cellCount),\n velocityY: new Float32Array(cellCount),\n divergence: new Float32Array(cellCount),\n pressure: new Float32Array(cellCount),\n pressureNext: new Float32Array(cellCount),\n vesselMask: null,\n tick: 0,\n time: 0,\n diagnostics: {},\n indexOf: grid.indexOf,\n };\n\n state.vesselMask = buildLampMask(state.indexOf);\n seedParticles(state, settings);\n return state;\n}\n\nexport function seedParticles(state, settings) {\n state.particles.length = 0;\n const center = (WIDTH - 1) / 2;\n\n for (\n let y = HEIGHT - 7.4;\n y <= HEIGHT - 2.1 && state.particles.length < settings.particleCount;\n y += 0.52\n ) {\n for (\n let x = center - 5.6;\n x <= center + 5.6 && state.particles.length < settings.particleCount;\n x += 0.52\n ) {\n if (Math.abs(x - center) >= lampHalfWidth(y) - 0.5) continue;\n const n = state.particles.length;\n state.particles.push({\n x: x + 0.06 * Math.sin(n * 1.7),\n y: y + 0.04 * Math.cos(n * 2.1),\n vx: 0,\n vy: 0,\n temperature: 0.2 + 0.035 * Math.sin(x * 1.9),\n });\n }\n }\n\n state.tick = 0;\n state.time = 0;\n}\n",[],[150,236,246],"1d87a5e4-2b2f-4b04-8da4-fcf63eba3723","settings.js","8aa47a82-8b55-11f1-84b0-1607ee4eb77e",273,["D",1785333493953],"export const defaultSettings = {\n particleCount: 220,\n heaterStrength: 0.12,\n coolingRate: 0.02,\n glassCoolingRate: 0.1,\n heaterFocus: 0.8,\n neutralTemperature: 0.5,\n densityResponse: 1.2,\n particleCohesion: 0.7,\n restDensity: 3,\n volumePressure: 0.9,\n pressureIterations: 60,\n timeStep: 1,\n substeps: 4,\n playbackRate: 6,\n};\n\nexport function copySettings(overrides = {}) {\n return { ...defaultSettings, ...overrides };\n}\n",[],[150,236,254],"409deb34-e9c7-4292-8258-2c73b3315eda","projection.js","b8d370d4-8b55-11f1-864d-1607ee4eb77e",278,["D",1785333571436],"import { HEIGHT, WIDTH } from \"../browser/config.js\";\n\nfunction sample(array, state, x, y) {\n const clampedX = Math.max(0, Math.min(WIDTH - 1, x));\n const clampedY = Math.max(0, Math.min(HEIGHT - 1, y));\n return array[state.indexOf(clampedX, clampedY)];\n}\n\nfunction computeDivergence(state) {\n for (let y = 0; y < HEIGHT; y++) {\n for (let x = 0; x < WIDTH; x++) {\n const horizontal =\n (sample(state.velocityX, state, x + 1, y) - sample(state.velocityX, state, x - 1, y)) *\n 0.5;\n const vertical =\n (sample(state.velocityY, state, x, y + 1) - sample(state.velocityY, state, x, y - 1)) *\n 0.5;\n state.divergence[state.indexOf(x, y)] = horizontal + vertical;\n }\n }\n}\n\nfunction depositParticleVelocities(state) {\n state.velocityX.fill(0);\n state.velocityY.fill(0);\n const weights = new Float32Array(WIDTH * HEIGHT);\n\n for (const particle of state.particles) {\n const x0 = Math.floor(particle.x);\n const y0 = Math.floor(particle.y);\n const tx = particle.x - x0;\n const ty = particle.y - y0;\n\n for (let offsetY = 0; offsetY <= 1; offsetY++) {\n for (let offsetX = 0; offsetX <= 1; offsetX++) {\n const x = Math.max(0, Math.min(WIDTH - 1, x0 + offsetX));\n const y = Math.max(0, Math.min(HEIGHT - 1, y0 + offsetY));\n const weight =\n (offsetX ? tx : 1 - tx) *\n (offsetY ? ty : 1 - ty);\n const index = state.indexOf(x, y);\n\n state.velocityX[index] += particle.vx * weight;\n state.velocityY[index] += particle.vy * weight;\n weights[index] += weight;\n }\n }\n }\n\n for (let index = 0; index < weights.length; index++) {\n if (!weights[index]) continue;\n state.velocityX[index] /= weights[index];\n state.velocityY[index] /= weights[index];\n }\n}\n\nfunction solvePressure(state, iterations) {\n computeDivergence(state);\n state.pressure.fill(0);\n state.pressureNext.fill(0);\n\n for (let iteration = 0; iteration < iterations; iteration++) {\n for (let y = 0; y < HEIGHT; y++) {\n for (let x = 0; x < WIDTH; x++) {\n state.pressureNext[state.indexOf(x, y)] =\n (sample(state.pressure, state, x - 1, y) +\n sample(state.pressure, state, x + 1, y) +\n sample(state.pressure, state, x, y - 1) +\n sample(state.pressure, state, x, y + 1) -\n state.divergence[state.indexOf(x, y)]) /\n 4;\n }\n }\n\n const previous = state.pressure;\n state.pressure = state.pressureNext;\n state.pressureNext = previous;\n }\n\n for (let y = 0; y < HEIGHT; y++) {\n for (let x = 0; x < WIDTH; x++) {\n const index = state.indexOf(x, y);\n state.velocityX[index] -=\n 0.5 *\n (sample(state.pressure, state, x + 1, y) -\n sample(state.pressure, state, x - 1, y));\n state.velocityY[index] -=\n 0.5 *\n (sample(state.pressure, state, x, y + 1) -\n sample(state.pressure, state, x, y - 1));\n }\n }\n}\n\nfunction enforceGridBoundaries(state) {\n for (let y = 0; y < HEIGHT; y++) {\n state.velocityX[state.indexOf(0, y)] = 0;\n state.velocityX[state.indexOf(WIDTH - 1, y)] = 0;\n }\n\n for (let x = 0; x < WIDTH; x++) {\n state.velocityY[state.indexOf(x, 0)] = 0;\n state.velocityY[state.indexOf(x, HEIGHT - 1)] = 0;\n }\n\n for (let y = 0; y < HEIGHT; y++) {\n for (let x = 0; x < WIDTH; x++) {\n const index = state.indexOf(x, y);\n if (!state.vesselMask[index]) {\n state.velocityX[index] = 0;\n state.velocityY[index] = 0;\n }\n }\n }\n}\n\nfunction sampleProjectedVelocity(state, particle) {\n const x0 = Math.floor(particle.x);\n const y0 = Math.floor(particle.y);\n const tx = particle.x - x0;\n const ty = particle.y - y0;\n let velocityX = 0;\n let velocityY = 0;\n\n for (let offsetY = 0; offsetY <= 1; offsetY++) {\n for (let offsetX = 0; offsetX <= 1; offsetX++) {\n const x = Math.max(0, Math.min(WIDTH - 1, x0 + offsetX));\n const y = Math.max(0, Math.min(HEIGHT - 1, y0 + offsetY));\n const weight =\n (offsetX ? tx : 1 - tx) *\n (offsetY ? ty : 1 - ty);\n const index = state.indexOf(x, y);\n\n velocityX += state.velocityX[index] * weight;\n velocityY += state.velocityY[index] * weight;\n }\n }\n\n return { x: velocityX, y: velocityY };\n}\n\nexport function projectParticleMotion(state, settings) {\n depositParticleVelocities(state);\n solvePressure(state, settings.pressureIterations);\n enforceGridBoundaries(state);\n\n for (const particle of state.particles) {\n const projected = sampleProjectedVelocity(state, particle);\n particle.vx = particle.vx * 0.52 + projected.x * 0.48;\n particle.vy = particle.vy * 0.52 + projected.y * 0.48;\n }\n}\n",[],[150,236,262],"d09791d9-b992-4a0b-b476-6da19488ddd2","particles.js","b6c69ea6-8b55-11f1-8977-1607ee4eb77e",277,["D",1785333568006],"import { HEIGHT, WIDTH } from \"../browser/config.js\";\nimport { collideWithLamp } from \"./geometry.js\";\n\nexport function applyParticleForces(state, settings, deltaTime) {\n for (const particle of state.particles) {\n particle.vy +=\n (settings.neutralTemperature - particle.temperature) *\n settings.densityResponse *\n 0.24 *\n deltaTime;\n particle.vx *= 0.992;\n particle.vy *= 0.992;\n }\n\n for (let a = 0; a < state.particles.length; a++) {\n for (let b = a + 1; b < state.particles.length; b++) {\n const first = state.particles[a];\n const second = state.particles[b];\n const dx = second.x - first.x;\n const dy = second.y - first.y;\n const distanceSquared = dx * dx + dy * dy;\n if (distanceSquared < 0.01 || distanceSquared > 2.25) continue;\n\n const distance = Math.sqrt(distanceSquared);\n const averageTemperature = (first.temperature + second.temperature) * 0.5;\n const phaseCohesion = 0.22 + 0.78 * (1 - averageTemperature);\n const force =\n (distance - 0.58) *\n 0.032 *\n settings.particleCohesion *\n phaseCohesion *\n deltaTime;\n const forceX = (force * dx) / distance;\n const forceY = (force * dy) / distance;\n\n first.vx += forceX;\n first.vy += forceY;\n second.vx -= forceX;\n second.vy -= forceY;\n }\n }\n}\n\nexport function applyParticleVolumePressure(state, settings, deltaTime) {\n const smoothingRadius = 1.3;\n const density = new Float32Array(state.particles.length);\n let maximumDensity = 0;\n\n for (let a = 0; a < state.particles.length; a++) {\n density[a] = 1;\n\n for (let b = a + 1; b < state.particles.length; b++) {\n const first = state.particles[a];\n const second = state.particles[b];\n const dx = second.x - first.x;\n const dy = second.y - first.y;\n const distance = Math.sqrt(dx * dx + dy * dy);\n if (distance >= smoothingRadius) continue;\n\n let weight = 1 - distance / smoothingRadius;\n weight *= weight;\n density[a] += weight;\n density[b] += weight;\n }\n }\n\n for (const value of density) maximumDensity = Math.max(maximumDensity, value);\n\n for (let a = 0; a < state.particles.length; a++) {\n for (let b = a + 1; b < state.particles.length; b++) {\n const first = state.particles[a];\n const second = state.particles[b];\n const dx = second.x - first.x;\n const dy = second.y - first.y;\n const distance = Math.sqrt(dx * dx + dy * dy);\n if (distance < 0.001 || distance >= smoothingRadius) continue;\n\n const averageDensity = (density[a] + density[b]) * 0.5;\n const excessDensity = Math.max(0, averageDensity - settings.restDensity);\n const hardCoreRepulsion = Math.max(0, 0.48 - distance) * 2;\n const pressure =\n (excessDensity * (1 - distance / smoothingRadius) * 0.055 +\n hardCoreRepulsion * 0.12) *\n settings.volumePressure *\n deltaTime;\n const forceX = (pressure * dx) / distance;\n const forceY = (pressure * dy) / distance;\n\n first.vx -= forceX;\n first.vy -= forceY;\n second.vx += forceX;\n second.vy += forceY;\n }\n }\n\n return maximumDensity;\n}\n\nexport function moveParticles(state, deltaTime) {\n for (const particle of state.particles) {\n particle.x += particle.vx * deltaTime;\n particle.y += particle.vy * deltaTime;\n collideWithLamp(particle);\n }\n}\n\nexport function rasterizeParticles(state) {\n state.wax.fill(0);\n state.temperature.fill(0);\n\n for (const particle of state.particles) {\n const x = Math.max(0, Math.min(WIDTH - 1, Math.round(particle.x)));\n const y = Math.max(0, Math.min(HEIGHT - 1, Math.round(particle.y)));\n const index = state.indexOf(x, y);\n state.wax[index] = Math.min(1, state.wax[index] + 0.32);\n state.temperature[index] = Math.max(state.temperature[index], particle.temperature);\n }\n}\n",[],[150,236,270],"da779fb8-0d28-455c-ad85-0dcb7040e179","geometry.js","8cce612e-8b55-11f1-be8d-1607ee4eb77e",274,["D",1785333497586],"import { HEIGHT, WIDTH } from \"../browser/config.js\";\n\nexport function lampHalfWidth(y) {\n const t = Math.max(0, Math.min(1, y / (HEIGHT - 1)));\n return 4.5 + 6.2 * Math.pow(Math.sin(Math.PI * t), 0.72);\n}\n\nexport function buildLampMask(indexOf) {\n const mask = new Uint8Array(WIDTH * HEIGHT);\n const center = (WIDTH - 1) / 2;\n\n for (let y = 0; y < HEIGHT; y++) {\n for (let x = 0; x < WIDTH; x++) {\n mask[indexOf(x, y)] =\n y > 0 && y < HEIGHT - 1 && Math.abs(x - center) <= lampHalfWidth(y) ? 1 : 0;\n }\n }\n\n return mask;\n}\n\nexport function collideWithLamp(particle) {\n const center = (WIDTH - 1) / 2;\n const minimumY = 1.35;\n const maximumY = HEIGHT - 2.05;\n\n particle.y = Math.max(minimumY, Math.min(maximumY, particle.y));\n if (particle.y === minimumY && particle.vy < 0) particle.vy *= -0.18;\n if (particle.y === maximumY && particle.vy > 0) particle.vy *= -0.12;\n\n const horizontalLimit = lampHalfWidth(particle.y) - 0.48;\n if (particle.x < center - horizontalLimit) {\n particle.x = center - horizontalLimit;\n particle.vx = Math.abs(particle.vx) * 0.2;\n }\n if (particle.x > center + horizontalLimit) {\n particle.x = center + horizontalLimit;\n particle.vx = -Math.abs(particle.vx) * 0.2;\n }\n}\n",[],[150,236,278],"39d7cd22-a1b7-41ac-b197-47f50b19dfa8","diagnostics.js","bbd76092-8b55-11f1-b641-1607ee4eb77e",279,["D",1785333576506],"import { HEIGHT } from \"../browser/config.js\";\n\nexport function measureSimulation(state, maximumDensity) {\n let averageTemperature = 0;\n let heightSum = 0;\n let maximumSpeed = 0;\n\n for (const particle of state.particles) {\n averageTemperature += particle.temperature;\n heightSum += 1 - particle.y / (HEIGHT - 1);\n maximumSpeed = Math.max(maximumSpeed, Math.hypot(particle.vx, particle.vy));\n }\n\n const particleCount = state.particles.length || 1;\n return {\n tick: state.tick,\n particleCount: state.particles.length,\n averageTemperature: averageTemperature / particleCount,\n waxHeight: heightSum / particleCount,\n maximumSpeed,\n maximumDensity,\n };\n}\n",[],[150,236,286],"b99a0b6b-59b7-4f82-8ffb-9b85d7bec8a1",272,["D",1785333456767],[174,175,176,177,178,179,180,181],[150,236],"12e287b6-ab33-4117-a800-3c6396eeaad4","renderer.js","d2c64be2-8b55-11f1-a328-1607ee4eb77e","18484c56-8a98-11f1-acc0-1607ee4eb77e",281,["D",1785333614966],"import { CELL, HEIGHT, WIDTH } from \"./config.js\";\nimport { lampHalfWidth } from \"../simulation/geometry.js\";\n\nexport function createRenderer(canvas) {\n const context = canvas.getContext(\"2d\");\n\n function render(state) {\n context.fillStyle = \"#090d13\";\n context.fillRect(0, 0, canvas.width, canvas.height);\n\n drawGrid();\n drawLamp();\n drawParticles(state);\n }\n\n function drawGrid() {\n context.strokeStyle = \"#1d2733\";\n context.lineWidth = 1;\n for (let x = 0; x <= WIDTH; x++) {\n context.beginPath();\n context.moveTo(x * CELL, 0);\n context.lineTo(x * CELL, HEIGHT * CELL);\n context.stroke();\n }\n for (let y = 0; y <= HEIGHT; y++) {\n context.beginPath();\n context.moveTo(0, y * CELL);\n context.lineTo(WIDTH * CELL, y * CELL);\n context.stroke();\n }\n }\n\n function drawLamp() {\n const center = (WIDTH - 1) / 2;\n context.beginPath();\n\n for (let y = 1; y < HEIGHT - 1; y++) {\n const x = center - lampHalfWidth(y);\n if (y === 1) context.moveTo(x * CELL, y * CELL);\n else context.lineTo(x * CELL, y * CELL);\n }\n for (let y = HEIGHT - 2; y >= 1; y--) {\n const x = center + lampHalfWidth(y);\n context.lineTo(x * CELL, y * CELL);\n }\n\n context.closePath();\n context.fillStyle = \"rgba(35, 65, 90, 0.14)\";\n context.fill();\n context.strokeStyle = \"#526477\";\n context.lineWidth = 2;\n context.stroke();\n }\n\n function drawParticles(state) {\n for (const particle of state.particles) {\n const temperature = particle.temperature;\n const red = Math.round(160 + temperature * 90);\n const green = Math.round(55 + temperature * 45);\n const blue = Math.round(180 - temperature * 70);\n\n context.beginPath();\n context.arc(particle.x * CELL, particle.y * CELL, 5.4, 0, Math.PI * 2);\n context.fillStyle = `rgb(${red}, ${green}, ${blue})`;\n context.fill();\n }\n }\n\n return { render };\n}\n\nexport function renderDiagnostics(diagnostics) {\n document.getElementById(\"tickMetric\").textContent = diagnostics.tick;\n document.getElementById(\"particleMetric\").textContent = diagnostics.particleCount;\n document.getElementById(\"temperatureMetric\").textContent =\n diagnostics.averageTemperature.toFixed(2);\n document.getElementById(\"heightMetric\").textContent =\n Math.round(diagnostics.waxHeight * 100) + \"%\";\n document.getElementById(\"speedMetric\").textContent =\n diagnostics.maximumSpeed.toFixed(2);\n document.getElementById(\"densityMetric\").textContent =\n diagnostics.maximumDensity.toFixed(1);\n}\n",[],[150,307,299],"browser","99efe816-cc1f-47eb-826a-14d16620ce76","grid.js","ff57144c-8a98-11f1-9ff2-1607ee4eb77e",256,["D",1785252514857],"export function createGrid(width, height, field) {\n function indexOf(x, y) {\n return y * width + x;\n }\n\n function at(x, y) {\n return field[indexOf(x, y)];\n }\n\n function set(x, y, value) {\n field[indexOf(x, y)] = Math.max(0, Math.min(1, value));\n }\n\n return { indexOf, at, set };\n}\n",[],[150,307,309],"57520181-98db-49c7-9d74-d9f904cff695","config.js","fb6a58ee-8a98-11f1-950d-1607ee4eb77e",255,["D",1785252508284],"export const WIDTH = 28;\nexport const HEIGHT = 18;\nexport const CELL = 24;\n",[],[150,307,317],"bd192a26-8178-4f27-8c52-93f6b3d5cfe8","app.js","83f9cfba-8a98-11f1-b875-1607ee4eb77e",285,["D",1785333739756],4,"import { createRenderer, renderDiagnostics } from \"./renderer.js\";\nimport { copySettings } from \"../simulation/settings.js\";\nimport { createSimulationState } from \"../simulation/state.js\";\nimport { stepLavaLamp } from \"../simulation/step.js\";\n\nconst canvas = document.getElementById(\"field\");\nconst renderer = createRenderer(canvas);\nconst settings = copySettings();\nlet state = createSimulationState(settings);\nlet running = false;\nlet initializingControls = true;\nlet accumulator = 0;\nlet previousTime = 0;\n\nfunction runOneFrame() {\n const diagnostics = stepLavaLamp(state, settings);\n renderer.render(state);\n renderDiagnostics(diagnostics);\n}\n\nfunction resetSimulation() {\n running = false;\n accumulator = 0;\n document.getElementById(\"play\").textContent = \"play\";\n state = createSimulationState(settings);\n runOneFrame();\n}\n\nfunction updateSetting(input) {\n settings[input.dataset.setting] = Number(input.value);\n const output = document.getElementById(input.dataset.output);\n output.textContent = formatValue(input.dataset.format, Number(input.value));\n\n if (!initializingControls && input.dataset.setting === \"particleCount\") {\n resetSimulation();\n }\n}\n\nfunction formatValue(format, value) {\n if (format === \"percent\") return Math.round(value * 100) + \"%\";\n if (format === \"integer\") return String(Math.round(value));\n return value.toFixed(2);\n}\n\nfunction animationLoop(time) {\n const elapsedSeconds = previousTime ? Math.min(0.1, (time - previousTime) / 1000) : 0;\n previousTime = time;\n\n if (running) {\n accumulator += elapsedSeconds * settings.playbackRate;\n while (accumulator >= 1) {\n runOneFrame();\n accumulator--;\n }\n }\n\n requestAnimationFrame(animationLoop);\n}\n\ndocument.querySelectorAll(\"[data-setting]\").forEach((input) => {\n input.addEventListener(\"input\", () => updateSetting(input));\n updateSetting(input);\n});\ninitializingControls = false;\n\ndocument.getElementById(\"step\").addEventListener(\"click\", runOneFrame);\ndocument.getElementById(\"reset\").addEventListener(\"click\", resetSimulation);\ndocument.getElementById(\"play\").addEventListener(\"click\", () => {\n running = !running;\n document.getElementById(\"play\").textContent = running ? \"pause\" : \"play\";\n});\n\nrunOneFrame();\nrequestAnimationFrame(animationLoop);\n",[],[150,307,325],"efea0db5-813a-4c4b-9b5e-662afae10362",244,["D",1785252127214],[169,170,171,172],[150,307],["D",1784854699691],[168,173,182,185],[150],["D",1784854669144],{"_97":96,"_104":100},{"_97":96,"_98":-5,"_99":100,"_18":56,"_101":102,"_103":49},{"_13":86,"_32":87,"_43":42,"_88":44,"_89":-5,"_90":-5,"_91":-5,"_92":-5,"_93":-5,"_94":45,"_95":96},"ctx",{"_79":-5,"_124":378,"_379":380,"_381":382,"_383":49,"_384":49,"_385":49,"_386":25,"_387":-5,"_388":-7,"_389":-7,"_390":63,"_391":49,"_392":49,"_393":-5,"_394":49,"_395":49,"_396":49,"_397":-5},"ENV",{"_349":350,"_351":352,"_353":87,"_354":355,"_356":357,"_358":359,"_360":361,"_362":363,"_364":365,"_366":367,"_368":369,"_370":371,"_372":373,"_374":375,"_376":377},"REACT_APP_SENTRY_DSN","https://586020d86f05489db63a554690acf1e9@o1398359.ingest.sentry.io/6724499","RENDER_GIT_COMMIT","e87eb04e707cf64e7e532c8e8ec395f209e17f15","RENDER_GIT_BRANCH","POSTHOG_API_TOKEN","phc_nmoyuAkStEZuUp69rYlg1DZgrIt19Gx0Y4Hwf8tGgJP","POSTHOG_API_HOST","https://wart.val.town","WEB_API_TEMPLATE","https://{val}.web.val.run","APP_URL","https://www.val.town","MODULE_URL","https://esm.town","VANITY_WEB_API_TEMPLATE","https://{label}.val.run/","DENOLS_URL","https://lsp.val.town","NODE_ENV","production","CLOUDFLARE_TURNSTILE_SITE_KEY","0x4AAAAAACtaIZJH7s9rBMZ6","GOOGLE_CLIENT_ID","875989696899-jtsqkhlbdv5jrlsk8631p7ipjg3c6o62.apps.googleusercontent.com","STRIPE_PUBLISHABLE_KEY","pk_live_51N2zvWEpZTTLipIkVEwXrUG9AT0yeOOEYxszarZT1jpsZV58Ly6wlg3SltZpHN26CUalOBmUSY7adQRQiSkCZz2500qSXNkf8Y","API_URL","https://api.val.town",[],"preferencesKeybindings","default","preferencesTheme","light","preferencesFixers","preferencesCopilot","preferencesSelectionAi","preferencesCloseBrackets","preferencesChatPanelState","preferencesDprint","preferencesDenofmt","notificationCount","flagDenols","isBusinessOrgMember","businessOrgHandle","isBusinessOrgAdmin","isHigherTownieTier","navCollapsed","currentOrgId"]

Diff · v288