the study viewsscience · math · biology · engineering

Every idea has a shape. These are live.

16 interactive 3D explainers, each a tiny deterministic recipe your AI coding agent mints from a single sentence — honest geometry and honest physics, not a video — so "now show it edge-on" is just your next question. Each page pairs the live world with a short study: the idea, what to look for, the misconceptions it corrects, and the knobs to turn. Click any tile and its world opens right here. Below the views sits the engineering side: objects at literal millimetres, measured and sliced; engines and chariots assembled from named parts; a building dropped into a generated city.

science9 views · click a tile to open it live

Relativity, quantum mechanics, nuclear chains, storms — each a live volume or world computed from the honest physics, not a looping video.

Black Hole in mojulo's live world — A Schwarzschild black hole with its accretion disk, rendered by tracing real photon geodesics per pixel — gravitational lensing, the photon ring, Doppler beaming, and gravitational redshift, live and orbitable.
Black Holethe study →full-page →

A Schwarzschild black hole with its accretion disk, rendered by tracing real photon geodesics per pixel — gravitational lensing, the photon ring, Doppler beaming, and gravitational redshift, live and orbitable.

Galaxy in mojulo's live world — A structurally honest Milky Way — bar, logarithmic spiral arms, exponential disk, and real dust lanes — rendered as a true emission-and-absorption volume, not a scatter of sprites.
Galaxythe study →full-page →

A structurally honest Milky Way — bar, logarithmic spiral arms, exponential disk, and real dust lanes — rendered as a true emission-and-absorption volume, not a scatter of sprites.

Gravitational Waves in mojulo's live world — Two compact masses spiral together on a live spacetime membrane: the chirp, the merger, and the ringdown of a gravitational-wave event, with the strain rendered as geometry you can orbit.
Gravitational Wavesthe study →full-page →

Two compact masses spiral together on a live spacetime membrane: the chirp, the merger, and the ringdown of a gravitational-wave event, with the strain rendered as geometry you can orbit.

Atmospheric Scattering in mojulo's live world — Why the sky is blue, why sunsets are red, and why astronauts see a thin blue limb — one scattering integral, computed per pixel around a planet you can orbit.
Atmospheric Scatteringthe study →full-page →

Why the sky is blue, why sunsets are red, and why astronauts see a thin blue limb — one scattering integral, computed per pixel around a planet you can orbit.

Lightning Storm in mojulo's live world — A volumetric storm deck threaded with lightning: stepped leaders, return strokes, and sheet lightning glowing inside clouds dense enough to hide the bolt that lit them.
Lightning Stormthe study →full-page →

A volumetric storm deck threaded with lightning: stepped leaders, return strokes, and sheet lightning glowing inside clouds dense enough to hide the bolt that lit them.

Quantum Wavepacket in mojulo's live world — A quantum wavepacket as an evolving probability volume: watch |ψ|² travel, spread, slosh in a trap, and beat between box states — quantum time-evolution made visible.
Quantum Wavepacketthe study →full-page →

A quantum wavepacket as an evolving probability volume: watch |ψ|² travel, spread, slosh in a trap, and beat between box states — quantum time-evolution made visible.

Nuclear Reactor in mojulo's live world — A controlled fission chain reaction with working control rods: watch a supercritical core get caught by a SCRAM — or left to run away — with a live neutron-population readout.
Nuclear Reactorthe study →full-page →

A controlled fission chain reaction with working control rods: watch a supercritical core get caught by a SCRAM — or left to run away — with a live neutron-population readout.

Atom in mojulo's live world — An atom as it actually is: a nucleus wrapped in electron standing waves — orbitals with real nodal planes and phase — plus a volumetric mode that raymarches the true |ψ|² probability cloud.
Atomthe study →full-page →

An atom as it actually is: a nucleus wrapped in electron standing waves — orbitals with real nodal planes and phase — plus a volumetric mode that raymarches the true |ψ|² probability cloud.

Engines and Motors in mojulo's live world — A single-cylinder four-stroke engine in cutaway, running the full Otto cycle over two crank revolutions — intake, compression, power, exhaust — with poppet valves that breathe on cue and a spark at the top of compression.
Engines and Motorsthe study →full-page →

A single-cylinder four-stroke engine in cutaway, running the full Otto cycle over two crank revolutions — intake, compression, power, exhaust — with poppet valves that breathe on cue and a spark at the top of compression.

math5 views · click a tile to open it live

A complex function as terrain, curvature you can measure with an arrow, a cone you slice, a landscape a ball rolls down — the ideas a flat plot cannot hold.

Complex Functions in mojulo's live world — A complex function as a landscape: height is log|f(z)|, colour is the phase, so zeros sink into pits, poles erupt into spikes, and the whole behaviour of f is readable as terrain you can orbit.
Complex Functionsthe study →full-page →

A complex function as a landscape: height is log|f(z)|, colour is the phase, so zeros sink into pits, poles erupt into spikes, and the whole behaviour of f is readable as terrain you can orbit.

Parallel Transport in mojulo's live world — Carry an arrow around a closed loop on a sphere without ever turning it, and it comes back rotated.
Parallel Transportthe study →full-page →

Carry an arrow around a closed loop on a sphere without ever turning it, and it comes back rotated.

3D Surface Plot in mojulo's live world — The graph of z = f(x, y) as a landscape you can traverse, with a ball that rolls downhill along the negative gradient and traces its path — so critical points become terrain and optimisation becomes a ball finding the bottom of a basin.
3D Surface Plotthe study →full-page →

The graph of z = f(x, y) as a landscape you can traverse, with a ball that rolls downhill along the negative gradient and traces its path — so critical points become terrain and optimisation becomes a ball finding the bottom of a basin.

Conic Sections in mojulo's live world — A translucent double cone and a flat cutting plane, orbited together: tilt the plane and the bright curve where they meet turns from circle to ellipse to parabola to hyperbola, which is where those four curves come from.
Conic Sectionsthe study →full-page →

A translucent double cone and a flat cutting plane, orbited together: tilt the plane and the bright curve where they meet turns from circle to ellipse to parabola to hyperbola, which is where those four curves come from.

Galton Board in mojulo's live world — Balls fall through a triangle of pegs, bouncing left or right at every row, and pile into bins that grow into a bell curve — the binomial distribution assembled one coin flip at a time, with the normal curve it converges to drawn over the top.
Galton Boardthe study →full-page →

Balls fall through a triangle of pegs, bouncing left or right at every row, and pile into bins that grow into a bell curve — the binomial distribution assembled one coin flip at a time, with the normal curve it converges to drawn over the top.

biology2 views · click a tile to open it live

A cell you click through and a helix you can check against the textbook — 3D structure where a flat diagram flattens the point.

Cell Structure in mojulo's live world — A cell as a set of rooms, not a bag of soup: click through the organelles of an animal or plant cell suspended in translucent cytoplasm, each with its role on the label.
Cell Structurethe study →full-page →

A cell as a set of rooms, not a bag of soup: click through the organelles of an animal or plant cell suspended in translucent cytoplasm, each with its role on the label.

DNA Double Helix in mojulo's live world — A DNA double helix with real geometry and real chirality — author it from an actual base sequence and watch the complementary strand write itself, at B-DNA proportions you can check.
DNA Double Helixthe study →full-page →

A DNA double helix with real geometry and real chirality — author it from an actual base sequence and watch the complementary strand write itself, at B-DNA proportions you can check.

engineeringobjects · measured, sliced, assembled

The same recipes, pointed at engineering: a part at literal millimetres, an engine from named parts, a building dropped into a generated city. Click a tile and the artifact itself opens, live — the same world the workshop serves, drag to orbit, scroll to zoom; "how it was made" is the session that made it. Every number below was read off a real run by a machine gate, and the fine print says what no gate has seen.

A desk-edge headphone hook in mojulo's shaded view: an orange C-shaped clamp with a swept arm curling up at the front
the desk hook, to the slicerworkbench · 3MF · PrusaSlicerfull-page →how it was made ▸
A grey V8 engine blockout in mojulo's live world: two banks of heads and covers, headers, an intake manifold and throttle body on top
the V8, ten partsassembler · code · Blenderfull-page →how it was made ▸
Two Roman racing chariots side by side in mojulo's live world: Claude Code's with a red breastwork and gold medallion, Grok Build's with a brown D-shaped body, both on eight-spoke wheels
the chariot, two agentsone brief · Claude Code · Grok Buildfull-page →how it was made ▸
A yellow worker robot spider-tank in mojulo's shaded view: six wheeled legs bent at the knee, an upright rear tank, a white three-dot camera head
the spider-tank, in segmentsthree segments · one assemblyfull-page →how it was made ▸
A generated city block in mojulo's shaded view: two crossing streets with cars and trees, a park with benches, and a five-story building on the corner lot
the facade, into its cityedifice · fractal cityfull-page →how it was made ▸
A hydroelectric dam's spillway in flood on a moonless night in mojulo's live world: twelve gates each shedding a white veil of water under warm crest lights, a ridge behind
the dam, one energy chainhydro view · measure_viewfull-page →how it was made ▸

Make it, measure it, slice it

A desk-edge headphone hook is one workbench recipe: a C-shaped profile extruded along the desk edge and a swept arm curling up at the front, authored in millimetres so the export reads the units instead of guessing them. Before anything leaves, measure_solid reads the numbers off the stored recipe — bounds, printed size, a closure audit, the Manifold union's volume and genus, and print advisories for thin walls, tiny features and an oversized bed. "Make the jaw 25 mm" edits one field on the same ref; nothing is re-minted. The export writes a 3MF with the units in the file, and a local PrusaSlicer runs headless and stamps what it saw: whether the sliced size agrees with the recipe's, whether the shell is manifold, the layers, the time.

recipe         415 bytes · one extrude, one sweep · units mm
edit           jaw 19 → 25 mm on the same ref (update_sketch)
measure_solid  closed · union 16,324 mm³ · genus 0 · no advisories
3MF            81 × 30 × 33 mm · units in the file · colour as basematerials
PrusaSlicer    2.9.6, headless · size agrees · manifold
               110 layers at 0.3 mm · 48 min · no supports
on record      sliced, and opened in the slicer — never printed

The first slice of this hook failed: the slicer counted three parts where there should be one. The fault was the kernel's — an end cap fanned from a centroid that sits in the C's open slot — and it was fixed there, with the recipe unchanged, the way the lounge's couch was. The operator owns the recipe; the maintainer owns the kernel; neither touches an export by hand.

An engine as parts, not a picture

The mechanics view can show a four-stroke engine running in cutaway. The V8 is the other direction: an engine built as ten named parts and assembled by relation. The block is one field solid — skirt, two banks, eight bores subtracted in field space. The crankshaft and the pistons with their rods are programs, a seeded loop that returns the part, because eight of a thing is a loop, not eight recipes. The assembler seats each part on another by on and gap, mirrors the second bank with flip, and freezes every part inline, so the recipe is whole. Move the placement numbers and the same recipe is the exploded view. Blender received it as an art-pass pack whose gate ran green, Cycles told the metals apart, and a derived clip shows the parts flying together and the pistons running through two revolutions.

The chariot is the same lesson as a brief in mojulo's orientation gallery: build a Roman racing biga from named workbench parts, assemble it, take it apart, hand the recipe on. The brief carries no solution, only exits — a machine exit and an eyes exit per phase. Claude Code filed the first signature. Then Grok Build took the same brief cold, with nothing but the gallery's get_work, and filed its own. Signatures are compared on structure, never on geometry, and touring one ends by deconstructing it, so a different host's agent proves every piece of a stranger's chariot is knowable from the recipe alone. The spider-tank is the working-object version: three workbench segments, one assembly, and five revisions that each re-mint only the segment that changed.

V8             10 parts · 13 placements · no warnings
               the block one field solid · crank and pistons two programs
chariot        Claude Code: 6 parts · 7 placements · one flaw caught by eye, fixed in place
               glb, stl, and a Godot pack whose gate ran clean
               Grok Build, cold, same brief: 7 parts · own flaw found and fixed · glb, stl
spider-tank    3 segments → an 8-item assembly → 5 versions, each re-minting one segment

Math that becomes a part

The math shelf above says the surface is the function. On the workbench the part can be the function too. A fields solid composes in distance-field space and is polygonized once: add, subtract and intersect over spheres, boxes, capsules and the lathe, extrude and sweep twins; blend for the smooth joins; shell, round, a stroke dabbed in or out, seeded displace for organic detail. A bored flange is genus one by construction. An expr term is a signed-distance expression in a small GLSL-like grammar with named dials — a gyroid slab whose t is wall thickness in world units, a bolt circle by polar mod, a twisted box, a fillet by smin — and six domain operators warp whatever came before: transform, repeat on a grid or around an axis, twist, bend, taper, elongate. When a part is a rule rather than a shape, mint_solid has a code kind: a short program in a fenced realm with no clock, no IO and a seeded random, returning the workbench spec or the faces. The program is stored as a parameter of the recipe, so it re-renders like everything else.

  • a flange 80 mm across with six M6 bolt holes on a 60 mm circle, 8 mm thick
  • a gyroid slab, a 40 mm cube with 1.2 mm walls — now 1.6
  • a bracket with a 12 mm bore, filleted where the web meets the base
  • a spiral staircase of fourteen treads, as a program I can re-run at 5 m tall

Buildings, and the city around them

An edifice is a building as a graph of masses placed by relation, floors at eleven feet, facades as material times rhythm — glass, brick or concrete in curtain, punched, banded, pier or grid — and roofs pitched or flat. The facade study here was a 308-byte brick-punched recipe, five floors on a 60 by 40 foot plot, iterated in place to a glass curtain and then to banded concrete under a shed roof. The generated city then takes it: compose_world with edifices lets a designed building claim a parcel in the fractal city. The planner tries every generated lot, evicts the fewest neighbours, and routes streets, sidewalks and props around the plot, while the building stays its own recipe, so editing the facade re-renders the city. The lit lounge on the home page is the interior half of the same story: a twelve-line floor plan, nine pot lights that travel as candela in the glTF, and three engines each checked on what they built from it.

edifice        308 bytes · brick punched · 5 floors · 60 × 40 ft
               two facade edits on the same ref
city inset     placement lot · yaw 0 · one generated building replaced · every street kept

The engineering shelf the catalog leaves in the workshop

The featured views above are the ones whose idea is three-dimensional in its bones. The package carries an engineering shelf beside them, mintable in any workshop. The hydro view tells hydroelectric power in five arcs of one kind — the dam's hydrostatic pressure and its Torricelli jet, the penstock trading height for speed, a Pelton runner spun by jet momentum, a generator's poles sweeping copper, and the whole plant in one world — with every arc quoting the same numbers from one energy chain, so doubling the head changes all five. The rocket view flies a Falcon-9-class mission on a standard atmosphere and real forces: gravity turn, max-Q throttle bucket, stage separation, boostback, entry burn, and the hoverslam that minimum thrust forces. The airplane view flies an A320-class hop on the four forces, or cuts the engines at cruise and glides. The mechanics view runs from the six simple machines and their work bars through gear trains, a screw jack and a crane to steam, four-stroke and inline-four engines, DC and AC motors, a quadcopter, a submarine and a ball in real air. Each has a measure_view read-back in SI units, and it refuses to report numbers for a view whose units are only for show. A photograph can come in the other way: capture_reference with the object target reads one object into workbench parts, heights as fractions of the whole, and mints it as a block-out.

  • teach how a hydroelectric dam makes electricity at 60 m head — now double the head
  • fly a Falcon 9 booster back to the pad; show me thrust, drag and dynamic pressure through max-Q
  • an A320 hop, then the same flight with the engines cut at cruise
  • a screw jack lifting an engine block; show the work in and the work out

Written by the tree's own rules. Sliced and print-ready are true; nothing on this page has been through a printer. True scale applies to the literal profile only — workbench, assembler, carved, turntable, vehicle — while views and worlds print as maquettes fit to a size. Closure and union audits advise and stamp; none refuses, and none guarantees a watertight shell. Godot is the first-class engine leg; Unity and Unreal are gated legs with their own ledgers, never identical. One non-Claude host drove one brief cold, and that is one data point, filed. As of September 2026.

how to use itscience concepts as live 3D, from a sentence

Ask for the concept, not the picture

Mojulo is an MCP server for the coding agent you already run — Claude Code or Codex. Once it is installed (npx mojulo init), you describe the idea in a sentence and the agent picks the view and sets its knobs. What comes back is a self-contained three.js page at a URL: drag to orbit, scroll to zoom, export it as one HTML file. Every page on this site was minted that way, and the parameter manual under each world is the real list of knobs.

  • show me a Schwarzschild black hole with its accretion disk, then take me around the far side
  • a reactor core that SCRAMs — now the same seed with the rods left out
  • argon's electron configuration, then hydrogen's 3d orbital as a probability cloud
  • z² as a complex landscape; now the same for (z²−1)/(z²+1)
  • carry an arrow around a triangle on a sphere and show me the holonomy

Recipes are starting points

Nothing here is a stored render. Each world is regrown on every open from a recipe a few lines long — a kind, a scenario, a handful of numbers — and that recipe is what your agent edits when you ask for a change. Underneath, the kinds share a small set of primitives: a Newtonian motion vocabulary (velocity, acceleration, gravity, trajectories sampled at equal time steps so a body's visible speed encodes its acceleration), orbital mechanics with a real ephemeris, wave math computed on a grid (the ripple tank's interference field, a wavepacket's |ψ|² volume, heat diffusing across a sphere), and per-pixel raymarching for volumes and for light bent by gravity. A scenario that does not exist yet is a code change in an open-source package, not a new product — the same primitives are there to build it from.

The site publishes the views whose idea is three-dimensional in its bones. The package carries more — projectiles and pendulums, orbits and comets, fission and fusion, the full math shelf — and every one of them can be minted fresh in a workshop.

A generalist's best effort, as of September 2026. The physics is honest where a page says it is and simplified everywhere else; these are textbook-level explainers, not research instruments, and each page's "Getting it right" section names what its render leaves out. If a view gets something wrong, an issue on the repository is the right place to say so.