New apps
New interactive apps appear almost every day: simulations, 3D models and tools to try, for school, university and professional learning. Here they are with the date they were built, newest first.
These weeks
A room with a window, a red and a green wall, rendered by path tracing: with 0 bounces only a hard patch of light, from one bounce the room brightens and the floor takes on the wall colours. Trace rays with a tap, change the sun and wall colours, noise versus averaging over time, proxy scene as a principle picture. Recreated, not Unreal Engine software.
Computer scienceTry it
A rock with 12.6 million triangles, split into clusters of 128 triangles: each cluster is drawn just fine enough that its error stays below one pixel. As you fly closer the coloured clusters break into finer ones live; roughly as many triangles are drawn as there are pixels. Comparison with classic LOD, seams, frozen selection. Principle recreated, not Unreal Engine software.
Computer scienceTry it
A courtyard is rendered pass by pass as in modern real-time engines: geometry, depth, G-buffer, shadow map, per-pixel lighting, occlusion, reflections, bloom, tonemapping, anti-aliasing. Every intermediate image is computed from the scene; a time budget shows what 16.7 ms at 60 fps means. Recreated for illustration, not Unreal Engine software.
Computer scienceTry it
An angled pane of glass reflects a hidden, brightly lit figure onto the stage as a transparent ghost. Control stage and pit light separately, reflection after Fresnel, ray path and virtual image; scenes Theatre 1862, Haunted Mansion 1969 and foil today. Seen from the side, the trick falls apart.
Architecture & scenographyTry it
An exhibition hall in 3D with three listening stations: omni speakers, directional speakers, sound domes and ultrasonic beams set, through directivity and reverberation time, where one station clearly leads and where stations overlap. The floor map shows sound islands, signal-to-noise ratio, level and speech intelligibility (STI); wavefronts and reverberation travel visibly through the hall. “All louder” leaves the map unchanged, directivity and damping create islands; at the visitor’s spot the mix is audible in space.
Architecture & scenographyTry it
A network of operators with live previews renders real-time graphics: noise, audio-reactive rings, feedback spirals and thousands of instances. Move the view to an intermediate node or cut a wire and see how TouchDesigner only cooks what is requested. Six families, converters, references and cost per frame.
Film & mediaTry it
A polyphonic synthesizer as a signal chain of source, filter, VCA and effects: subtractive, FM, wavetable, sampler and granular, with envelopes, LFOs and a modulation matrix. A 3D waterfall spectrogram shows live how the filter cuts away overtones, or how a sample played an octave higher becomes twice as high and half as long. Eleven sound design recipes explain why it sounds that way.
Music (Gymnasium)Try it
Church 537, new dome 562, mosque from 1453, museum from 1934, mosque again from 2020: timeline with minarets and buttresses by date, furnishings for each use. Section with load path through pendentives and semi-domes, collapse of 558, view up into the floating dome with light through the ring of windows; surroundings from OpenStreetMap.
World heritage & building historyTry it
From Old St Peter's via Bramante, Raffael, Sangallo and Michelangelo to Maderno and Bernini: timeline 324 to today, designs morph into each other, plan as an architectural drawing, the Vatican today from OpenStreetMap. The view from the square at eye level measures why the façade hides Michelangelo's dome from close up – and how much a central plan would have shown.
World heritage & building historyTry it
The Parthenon has almost no straight lines: curved steps and entablature, swelling columns tilted inwards, thicker corner columns and narrower corner bays. A slider exaggerates the deviations up to 100 times until you see them; measuring lines, axes up to their meeting point about 2.3 km up, theories about the purpose side by side, paint as a reconstruction.
World heritage & building historyTry it
The complex from OpenStreetMap with the planning grid after Koch: charbagh garden, water axis and reflecting pool, mausoleum by the river rather than in the middle of the garden. Axial view from the great gate with reflection, section with the hidden inner dome, sun across the day and year. The only asymmetry: Shah Jahan's cenotaph.
World heritage & building historyTry it
Pantheon, Hagia Sophia, Florence Cathedral, St Peter's, Taj Mahal and St Paul's as sections at the same scale: side by side, overlaid or one at a time, with a person for scale. The span has hardly grown since the Pantheon; progress lies in construction and height. The Forces switch shows compression, hoop tension, thrust and what resists it.
World heritage & building historyTry it
The Forum as a working model on the real ground plan: a time slider from the regal period via Campo Vaccino to today, buildings appear and disappear, a ground section shows the metres of fill. Every building with dating, dimensions, source and degree of certainty (standing, excavated, reconstruction); today's buildings from OpenStreetMap.
World heritage & building historyTry it
One square kilometre each from OpenStreetMap at the same scale: Rome, Venice, Stone Town, Barcelona, Manhattan, Paris, Stuttgart and Reutlingen. Figure-ground, streets or both, metrics such as built-up area and block size, plus the street rosette with orientation order after Boeing: grids show a cross, grown cities a circle.
World heritage & building historyTry it
3D exhibition floor plan with visitors following the social force model: a tour with a highlight, a bottleneck with a door and counterflow, and the evacuation of a hall through one exit. The floor shows density in Fruin levels; a fundamental diagram compares measured speed and flow with the Weidmann curve. The list of evacuations shows that pushing creates arches in front of the door and lengthens the evacuation.
Architecture & scenographyTry it
Exhibition room in 3D with a desk or tall showcase, a draggable ceiling spotlight and a visitor. The reflection zone on the ceiling shows from where a spotlight appears as a reflection in the glass; the visitor-view panel shows what the visitor sees. Illuminance E = I·cos θ/d², annual exposure in lx·h and glare are checked live against guidelines after CIE 157.
Architecture & scenographyTry it
An exhibition hall in 3D with two listening stations: materials for floor, ceiling and walls set the reverberation time after Sabine and Eyring and the reverberation radius. The floor map shows where station A is ahead of B or where direct sound outweighs reverberation. Early reflections run as rays via image sources, and an impulse response and a synthetic listening test make the difference audible.
Architecture & scenographyTry it
A projector shines onto a room corner, a column, a sculpture of blocks or a facade. Four modes, uncorrected, keystone, mapping and illusion, show why keystone correction holds on one plane only, mapping fits every shape and a spatial illusion works only from the sweet spot. A panel shows the image the projector sends; lenses show brightness (cos θ / d²) and stretched pixels.
Architecture & scenographyTry it
Billiards in a convex table: for the ellipse, every orbit near the rim envelops a smooth caustic and the phase portrait is layered without gaps near the rim. Deform the table with Fourier waves and island chains and chaotic zones tear open between the curves; the Collar panel measures which orbits become wide. Near-boundary Birkhoff conjecture, openai/math family 147.
Open problems, solved by AITry it
Random triangles vanish from the complete graph one after another until none is left. The deleted triangles flash, the triangle-free leave glows. A series up to n = 2000 shows that the leave divided by n^1.5 tends to 1/(2√2) ≈ 0.354. openai/math family 188 (formalised in Lean).
Open problems, solved by AITry it
Radar pulses of + and − whose echo peaks only at exact alignment: flip squares, see the echo live and as a sliding animation, complete search over all lengths up to 48 (hits only at 2, 3, 4, 5, 7, 11, 13), circulant matrix with order 4 and a check of order 16. Result from openai/math (family 179, formalised in Lean): circulant Hadamard matrices exist only in orders 1 and 4.
Open problems, solved by AITry it
n points in the plane: how many lines through two of them split the rest exactly in half? Place and drag points, all halving lines glow live; Lovász's rotating line counts them as changes; record sets from a search; log-log chart against Dey's n^{4/3}. New: at most C·n^{4/3−ε}, openai/math family 183 (formalised in Lean).
Open problems, solved by AITry it
Every fraction a/b as a sum of distinct unit fractions: the greedy method against the shortest expansion, as a pie and a zoom cascade down to denominators with 25 digits. N(b) for all b ≤ 200 computed exactly, plus Erdős–Straus (4/n). Result from openai/math (family 025, formalised in Lean): the number of terms needed grows only like log log b, and that is best possible – Erdős problem 304.
Open problems, solved by AITry it
Cut the deck, one coin per pair: after log₂ N rounds every single card is uniform, the whole deck far from it. Animated shuffling, exact distance for 8 cards over all 40,320 orders, counting bound, riffle comparison, growth over d. Result from openai/math (family 238, formalised in Lean): Θ(log N) rounds suffice.
Open problems, solved by AITry it
n points in a square, the smallest triangle glows: how large can it be at most? Grid (area 0), random, Erdős parabola and random + delete compared, an optimiser lifts the smallest triangle, chart n²·Δ and exponent ladder. New: Δ(n) ≥ c·n^(−2+η) with η ≈ 3·10⁻²³⁶, the “almost n⁻²” conjecture is refuted. openai/math family 191 (formalised in Lean).
Open problems, solved by AITry it
Two random domino tilings on top of each other give nested loops of every size. Sampled exactly via the Temperley bijection, construction step by step, magnifier, lattice comparison: the large loops do not depend on the fineness. In the limit this is CLE₄ – proven as curves for the half-plane; openai/math family 226.
Open problems, solved by AITry it
Nine world expo buildings from 1851 to 2025 as 3D structures: Crystal Palace, Eiffel Tower, Atomium, Philips Pavilion, Fuller dome, Frei Otto’s cable net, Shigeru Ban’s paper pavilion, Seed Cathedral and the Grand Ring of Osaka. The Structure lens colours every member by compression, tension, bracing or bending; a construction slider shows assembly in modules, ring by ring or the paper-tube grid laid out flat and pushed up. On the site all stand at the same scale, enclosed by the Grand Ring; a timeline compares planned and actual lifetimes.
Architecture & scenographyTry it
Smoothly through 40 powers of ten: from the cosmic web past galaxy, Earth, city and leaf down to cell, DNA, atom and atomic nucleus. Each lens sits inside the previous one, a ruler shows the real gaps. "Pattern" lights up the same cell network in five worlds: same geometry, different causes.
Architecture & scenographyTry it
A vibrating surface has lines that stand still: sand gathers on them as on a Chladni plate. Spherical harmonics and torus waves up to level 14, rings, meridians, checkerboard or a random mixture, glowing nodal lines, length measured live. The chart shows that the length grows only like the frequency √λ, no faster. Yau's conjecture for smooth surfaces, plus the counterexamples in dimensions 3 to 5; openai/math family 350 (formalised in Lean). Exhibit-ready.
Open problems, solved by AITry it
A polyhedron with three edges at every vertex and only even faces always has a round trip that visits every vertex exactly once. A glowing thread searches for it live by backtracking: on the cube, a prism, Archimedean solids and random polyhedra with faces up to twelve vertices and more. Vertices in two colours, large faces tinted. Two counterexamples, each missing one condition (Tutte graph, three chambers), make the complete search fail. openai/math family 180 (formalised in Lean). Exhibit-ready.
Open problems, solved by AITry it
A Gaussian hill, glass walls that split it into sectors, and arrows for the Gaussian centroids of the cells: drag the walls, 2 to 6 sectors, shift the centre, compare half-space, tetrahedron, cube and octants in space. The measuring ring closes only for the propeller of three 120° sectors with value 9/(8π). Result from openai/math (family 096, formalised in Lean): no partition in any dimension gets above it. Exhibit-ready.
Open problems, solved by AITry it
How tightly can needles pointing in many different directions be pushed together? The Kahane construction as a bundle of 16, 256 or 4096 tubes: pushed together, the volume of the union shrinks, but only logarithmically slowly, more slowly than any power of the thickness δ. Glowing needle through all directions, chart 2D versus 3D, planar Besicovitch set. Result from openai/math (family 074): Kakeya maximal conjecture in 3D, full dimension in 4D. Exhibit-ready.
Open problems, solved by AITry it
The Riemann zeta function as a landscape over the critical strip: where it touches the floor there is a zero, each one carrying a light needle on σ = ½. Behind a glass wall at 7/8 lies the strip now proven zero-free, at every height; the old boundaries of 1899 and 1958 instead creep towards 1. Window up to t = 1000, prime consequence π(x) vs li(x). Result from openai/math (family 003, formalised in Lean); the Riemann hypothesis itself remains open. Exhibit-ready.
Open problems, solved by AITry it
A dome of heptagons, the {7,3} lattice of the hyperbolic plane: every edge is open with probability p. Between p_c and p_u several separate clusters reach the rim at once; on ℤ² it jumps straight from none to one. Dome, Poincaré disc and ℤ² comparison, counter and curve over p. Benjamini–Schramm 1996, proved for every nonamenable graph in openai/math, family 214 (formalised in Lean). Exhibit-ready.
Open problems, solved by AITry it
Many short arrows, each may be flipped: does the walk of partial sums stay in a ball of radius √d, however long it is? Random signs run off like √n, the greedy choice fails against an adversarial sequence, a search over the whole sequence stays inside. Sliders for steps (up to 2000) and dimension (2–12), charts over n and over d. Euclidean Steinitz–Bergström theorem, openai/math family 097 (formalised in Lean). Exhibit-ready.
Open problems, solved by AITry it
How little cross-section do cylinders need to cover a tetrahedron? Bang's two cylinders (1951) hit exactly half the smallest shadow area. Fanned out and slightly tilted, with matching side planes and a small margin, 2·⌈2/ε²⌉ cylinders get strictly below it. Choose tilt and sector count, see the exact cost, gap test with 120,000 points, coarse fanning tears. The gain is tiny but real. openai/math family 100 (formalised in Lean). Exhibit-ready.
Open problems, solved by AITry it
Liénard systems ẋ = y − F(x), ẏ = −x: limit cycles found live via the Poincaré return map. For deg F ≤ 5 there are at most two, and two are attained. Plus a degree-7 preview, the LMP conjecture and the bound H(n). openai/math family 143.
Open problems, solved by AITry it
Site percolation in a cube up to 64³: the largest cluster glows, p moves around p_c ≈ 0.3116. At p_c it often reaches wall to wall, yet its share shrinks towards 0 – there is no infinite cluster. openai/math family 213 (formalised in Lean).
Open problems, solved by AITry it
You block, the AI builds from a proof certificate: after at most 21 Maker moves the six-cell shape Snaky stands. Counter, zone, threats, second mode as Maker; openai/math family 187.
Open problems, solved by AITry it
A particle hops through a disordered lattice: does the wave spread or stay trapped? Eigenstates as a height field (2D) and a cube of spheres (3D), sliders for disorder, energy and lattice size, participation number and size comparison. In 2D every disorder localises, in 3D weak disorder allows spreading (preprint openai/math, family 261). Includes the honest finite-size trap at weak disorder in 2D.
Open problems, solved by AITry it
Fire on a random grid: the front becomes round, fastest routes merge into trees, and almost surely there is no route that is fastest and infinite in both directions (bigeodesic). openai/math, family 212.
Open problems, solved by AITry it
A symmetric body and its polar body: where one reaches far out, the other is narrow. Morph the cube into the ball and the octahedron, compare cylinders, zonotopes and a simplex with a movable centre – the gauge shows the volume product exactly. Cube and octahedron land exactly on the lower bound 32/3, the ball at the very top. Result from openai/math (family 087, formalised in Lean): |K||K°| ≥ 4ⁿ/n! in every dimension, equality exactly for Hanner bodies; in general the simplex is the minimum.
Open problems, solved by AITry it
Live Monte Carlo of the planar XY model: vortex pairs unbind at T_BKT ≈ 0.893, and exactly there correlations decay like r^(−1/4) (openai/math, family 216).
Open problems, solved by AITry it
Random points, Voronoi cells, a coin flip per cell: is there a path from left to right? Drag the corners, change the shape, compare Voronoi with the hexagonal lattice: the background counter lands on Cardy's prediction, which depends only on the conformal shape. In the triangle Carleson's line P = x holds. Result from github.com/openai/math (family 224, not formalised in Lean).
Open problems, solved by AITry it
Which region of given volume has the least surface area in a cube with glued faces? Drag the volume and watch the best shape jump from ball to tube to slab – at the thresholds 4π/81 and 1/π two shapes tie exactly. With periodic neighbour copies, a profile chart and complements for V > ½. Result from openai/math (family 354, formalised in Lean).
Open problems, solved by AITry it
Gaussian primes as stepping stones: with a fixed step size D the plane falls apart into islands. A walker runs from the origin to the moat, and a periodic sieve shows the proof idea. Result from openai/math (family 028, formalised in Lean): for every D all islands are uniformly bounded.
Open problems, solved by AITry it
An insulated plate is heated: where does the hottest point end up? The first Neumann eigenfunction as relief and heat map for a disc, ellipse, stadium, bean, star, a shape with a hole or your own drawing. Without holes the maximum and minimum lie on the boundary and there is no interior critical point (preprint openai/math, family 369). Heat flow with a track of the hot spot, eigenspace mix for a double eigenvalue.
Open problems, solved by AITry it
How few crossings does a drawing need in which every point is joined to every other? Drag vertices, flip arcs, let it search: at best the counter lands on the Harary–Hill or Zarankiewicz formula. With straight edges a gap remains from K₈ on; the two-page drawing hits the formula exactly. Result from github.com/openai/math (family 165, Lean-formalised).
Open problems, solved by AITry it
The kicked rotor p′ = p + K·sin θ, θ′ = θ + p′ on the torus: islands of order next to a sea of chaos. Turn the kick strength K, click orbits and watch their Lyapunov exponent converge, follow the chaotic area share over K, zoom into islands. On the result from github.com/openai/math (family 146): for every sufficiently large K, chaos has positive area, i.e. positive metric entropy (Sinai's conjecture).
Open problems, solved by AITry it
A ball rolls forever on a triangular billiard table. With rational angles it is confined to finitely many directions (the direction rose of the equilateral triangle has exactly 6 spokes). If one angle is irrational, it spreads evenly over position and direction, even in pairs (weak mixing). Drag corners, presets, fast forward, occupation map. Result from the preprint catalogue github.com/openai/math (family 150).
Open problems, solved by AITry it
How many colours does the plane need so that points at distance 1 never share a colour? Isbell's hexagons show that 7 suffice at the right size. A unit circle marks every same-coloured pair at distance 1; stripes, squares and 5-colour attempts visibly fail, and the Moser spindle and Golomb graph sit on the plane as unit-distance graphs. Result from the AI preprint catalogue openai/math (family 158, Lean-formalised): 5 colours never suffice, so the answer is 6 or 7.
Open problems, solved by AITry it
Mutually repelling particles at fixed density order themselves into a hexagonal honeycomb — for every completely monotone repulsion (Gaussian, Riesz, screened). Choose potential and range, relax from random or from a square lattice, watch defects and the circle packing; charts show that square, rectangular and rhombic lattices have more energy for every slider value. Cohn–Kumar conjecture in the plane, family 090 from github.com/openai/math (AI-generated preprint, main theorem formalised in Lean).
Open problems, solved by AITry it
An icosahedral capsid of 60·T subunits after Caspar and Klug: choose T = 1, 3, 4 or 7 and see that there are always exactly 12 pentamers while the hexamers increase. Self-assembly from a nucleus, symmetry axes (5-, 3-, 2-fold), the unfolded net with the step (h, k), envelope with spikes and a cut down to the genome. Exhibit-ready.
Biology & neuroscienceTry it
Protons flow through the membrane and turn a ring of c subunits; the γ stalk deforms the three β subunits in turn (open, loose, tight), and every turn makes three ATP. Change the gradient and the c-ring (c8, c10, c14), read the energy balance per ATP, run it backwards as a proton pump. Exhibit-ready.
Biology & neuroscienceTry it
A patch of cell membrane with an aquaporin tetramer: water passes four pores in single file, its dipole flips at the NPA motif, a proton is rejected. Set the solute gradient, open a cross-section, show NPA and the ar/R constriction, compare with the bare lipid bilayer. Exhibit-ready.
Biology & neuroscienceTry it
A motor protein goes for a walk: kinesin-1 walks hand over hand along a microtubule of α/β-tubulin to the plus end, 8 nm and one ATP per step, pulling a vesicle behind it. Set ATP concentration, opposing force and slow motion, count steps, distance and ATP, watch it stall at about 6.5 pN; dynein walks the other way for comparison. Exhibit-ready.
Biology & neuroscienceTry it
Four chains that help each other: as oxygen binds, the tetramer switches from the tense T to the relaxed R state, the dimers rotate by about 15° and 2,3-BPG drops out of the cavity. Adjust pO₂, pH (Bohr effect) and BPG, compare the S-shaped binding curve with myoglobin live and read how much O₂ reaches tissue and muscle. Exhibit-ready.
Biology & neuroscienceTry it
A model protein passes through primary, secondary, tertiary and quaternary structure in smooth transitions: bead chain with sequence, α-helix and β-sheet with hydrogen bonds, folded domain with hydrophobic core and disulfide bridge, tetramer of four chains. Colour by structure, polarity or chain; heating unfolds it into a random coil while the sequence stays. Exhibit-ready.
Biology & neuroscienceTry it
Cas9 with its guide RNA slides along a DNA double helix, checks every PAM site (NGG), unwinds the DNA and forms the R-loop. Only with full pairing do HNH and RuvC cut both strands 3 bp before the PAM. Then choose the repair: end joining (NHEJ) with an insertion or deletion, or precise copying from a template (HDR). A mismatch in the seed prevents the cut. Exhibit-ready.
Biology & neuroscienceTry it
How 2 m of DNA fit into a nucleus: five compaction levels of the same genetic material, each at its own scale — double helix, beads on a string (147 bp around a histone octamer, H1), 30 nm fibre as a model (solenoid/zigzag), loops on a protein scaffold, metaphase chromosome. Acetylation opens the chromatin and lets RNA polymerase in, methylation with HP1 compacts it. Exhibit-ready.
Biology & neuroscienceTry it
A figure demonstrates eight typical vocal warm-ups — hissing, impulses, yawn and sigh, humming, lip trill, siren on ng, vowel row, triad — and sings them in four voice types. On request look inside: diaphragm, lungs, larynx and mouth from real anatomical data (BodyParts3D) move with every breath and tone. Sing along with the microphone and see your pitch next to the target.
Music (Gymnasium)Try it
Vectors as arrows and as number pairs: shift arrows in parallel (same vector), a + b along both ways around the parallelogram, b − a and closed vector chains, multiples r·a flipping for r < 0, normalising, coordinates via e₁ and e₂ with the magnitude as Pythagoras — |a + b| ≤ |a| + |b| live.
Linear algebraTry it
r·a + s·b + t·c as a vector chain: the span is a line, a plane or all of space. Moving c into the plane of a and b collapses the space grid to a plane, det = 0 and a non-trivial zero chain appears. Decomposition mode F = r·a + s·b, graphically via the parallelogram and as a linear system.
Linear algebraTry it
Vectors beyond arrows: monthly sales as a vector in ℝ¹², position + velocity as a state in ℝ⁶. a + b, r·a and a·b component-wise, the dot product as a running sum, magnitude and cos φ as the similarity of two curves (b = 2·a ⇒ cos φ = 1), time step position + Δt·v in 3D.
Linear algebraTry it
A gas in a cylinder sits as the system in a water bath. Switch the type of system (open, closed, isolated) and the wall (diathermic, adiabatic); heat q and work w cross the boundary as visible energy packets. A ledger books q, w and ΔU with the Atkins sign convention; four examples from vacuum flask to car engine cylinder.
ChemistryTry it
An ideal gas expands isothermally in a thermostat bath along three paths: reversibly, against constant external pressure and freely into a vacuum. The p–V diagram shows the work as the area under the external pressure; in the lecture example that is −2.68, −1.62 and 0 kJ. Compression and multistage expansion are included.
ChemistryTry it
Proteins, ligands and complexes bind and dissociate in a 3D reaction space while concentrations and rates relax to equilibrium. Covers the conformational change A ⇌ A* and binding A + B ⇌ AB with k₊, k₋, Kd and the binding curve. Temperature, ΔH° and ΔS° link K to energy via ΔG° = −RT ln K.
ChemistryTry it
p–Vm–T state surface of CO₂ after van der Waals with coexistence region, critical point and ideal-gas comparison, next to a piston and cylinder in the particle picture. Isothermal compression shows condensation at constant vapour pressure below Tc and the supercritical fluid above it. The compression factor Z = pVm/(RT) quantifies the deviation from the ideal gas.
ChemistryTry it
A semi-transparent perch with a visible swim bladder and gas gland drifts in a 0–100 m water column, with force arrows, a pressure gauge and the V(p) hyperbola. By Boyle's law the bladder halves at 10 m depth and the fish keeps sinking until the gas gland refills it. Reeling it in fast expands the bladder up to barotrauma.
ChemistryTry it
Play to the click — on a pad, the table, a drum kit or e-drums. Every stroke is measured in milliseconds: timing track with a ±15 ms target band, tendency over the round (rushing/dragging from bar …), feedback and the next exercise. Input via microphone (analysed in the browser only), MIDI or tapping; room check and calibration against latency.
Music (Gymnasium)Try it
Explicit Euler step by step: read off the slope at the starting point, follow the tangent for one step size h, new point. The dashed solution curve through each point shows how the method jumps onto neighbouring curves and errors add up. Enter your own right-hand side f(x, y) or pick a preset (slide example, oscillation, growth, decay, logistic); slide the step size, compare with h/2 and h/4, read the error in a log-log plot — order 1, special cases and instability for too large h.
NumericsTry it
Assignment does not copy: Python programs run line by line, the names are in the middle and the objects on the right, and arrows show which name points to which object. After a = l1 there is one card and two arrows; a function call opens a frame with a third arrow to the same card. Five examples (two names, lists, rebinding, numbers, a real copy), and before every print the question “What does Python print?”.
Computer scienceTry it
Slow motion for Lauf(8.5, 53.5) and l.tempo(): the rewrite strip turns l.tempo() into Lauf.tempo(l); the object before the dot slides into the parentheses and becomes self. The constructor first creates an empty object and fills it through self; whatever is not attached to self disappears with the frame. Methods live only on the class card and two objects share them. Plus self passed in the call (TypeError) and the forgotten self. (AttributeError).
Computer scienceTry it
Class as a blueprint, objects as cards: create runs, set attributes by hand and compute the total distance. A typo silently creates a new attribute; Python only complains when it is read (with “Did you mean”). The __init__ switch shows how a constructor guarantees complete objects. The generated program behaves the same in real Python; four tasks.
Computer scienceTry it
A training log with an interface (eintragen, gesamtstrecke) and an X-ray view of its inside: three versions store the runs in completely different ways. The program that only uses the methods works in all three versions; the program that reaches into the inside breaks with the first rebuild. The underscore does not protect either; it is a request.
Computer scienceTry it
Which method does a * b call? A flow diagram shows the two stations a.__mul__(b) and b.__rmul__(a) with the exits result, NotImplemented and error. With numbers, strings, lists, fractions in four stages (isinstance, __rmul__, __eq__) and runs with and without __lt__: why 3 * Bruch(1, 2) first fails at the int and then ends up in __rmul__.
Computer scienceTry it
A tower of object, Wettkampf, Lauf and object: for w.tempo(), print(w) or l.platz a search beam climbs station by station, and the first match wins. tempo lives only in Lauf, all attributes sit in the one object, and super() continues the search one level up. Switching methods off shows which version of __str__ takes over, all the way up to object.
Computer scienceTry it
The number systems ℕ, ℤ, ℚ, ℝ and ℂ as a ladder: above a 3D number line stands the modulus of the equation, and a missing solution stays a hollow ring until the next system supplies it (5 + x = 2, 3·x = 5, x² = 2, x² = −2). A zoom closes in on √2; in ℂ the line unfolds into a plane, and the surface |z² + 2| touches the floor at ±i√2. In the end stage, rolled polynomials show the fundamental theorem of algebra: as many roots as the degree.
Complex numbersTry it
Proof of Euler's formula in eight steps: the Taylor series of eˣ only needs plus and times and therefore also works for complex numbers. With z = iφ every term turns another 90°, and the arrows form a spiral towards the unit circle. Sorted into terms without and with i, they become the series of cosine and sine, shown on a helix with cos and sin shadows. De Moivre's theorem follows at the end.
Complex numbersTry it
Steel-string, classical and electric guitar at true dimensions on stage: string × fret gives the note, the frets get closer towards the body, fret 12 halves the string. With chord shapes, a note finder, a capo and physically modelled sound.
Music (Gymnasium)Try it
A clickable keyboard over several octaves: note names (C D E F G A B), octave and frequency per key, the tone sounds. Semitones, octave, accidentals.
Music (Gymnasium)Try it
Choose two tones → interval name, semitone steps, frequency ratio (fifth 3:2). Playable melodically/harmonically — consonance vs. dissonance audible.
Music (Gymnasium)Try it
Root + scale (major, minor variants, church modes, pentatonic): construction on the keyboard, whole-tone/semitone step pattern, playable up/down.
Music (Gymnasium)Try it
Root + chord type (major/minor/diminished/augmented, seventh chords) + inversion: stacked construction from thirds, chord symbol, audible as an arpeggio/together.
Music (Gymnasium)Try it
The circle of the 12 major/minor keys at the interval of a fifth: click a key → accidentals, relative key and tonic/subdominant/dominant (T/S/D) highlighted.
Music (Gymnasium)Try it
See and hear close, drop-2, drop-3, rootless, quartal and shell voicings on a piano keyboard.
Jazz harmonyTry it
A step grid with kick/snare/hi-hat/clap: place beats, play at tempo, time signature 4/4 · 3/4 · 6/8. Accented beats and a running light show meter & groove.
Music (Gymnasium)Try it
Root → partials f, 2f, 3f … with intervals; individual overtones switchable (additive synthesis). Timbre = mixture of the partials, audible and visible.
Music (Gymnasium)Try it
Generate simple pop-inspired piano pieces with professional notation. Play through MIDI or microphone input while recognised notes are highlighted in the score.
Music (Gymnasium)Try it
Real skull scans of dog, wolf, cat, lion, brown bear and red deer: canines and carnassials, grinding molars, a jaw joint you can open and chew with. Plus walking skeletons: plantigrade, digitigrade and unguligrade, with a human alongside if you like.
Biology & neuroscienceTry it
Every representation and operation of complex numbers in one place: drag z and w in the complex plane and read or type the Cartesian, polar and Euler forms live. The angle trap shows where arctan(b/a) lands in the wrong quadrant. Addition shifts, multiplication rotates and stretches the whole plane, division rotates back, conjugation mirrors, powers form a spiral and roots a regular n-gon. Each result shows the Cartesian and the polar calculation side by side and marks the easier one. The ‘One number’ mode shows the building blocks of the conversion for a single z (legs a and b, pointer r, angle φ, unit circle) and converts step by step between Cartesian, polar and Euler form.
Complex numbersTry it
The indirect proof with tiles: 2q² = p² splits the p² square into two equal halves, odd squares always keep a middle tile, p = 2a quarters the square and q turns even, so the stamp “reduced” breaks and the same figure returns one step smaller. In Try mode, test your own fractions: even 99/70 misses by exactly one tile.
Visual proofsTry it
Two black holes orbit, merge and ring down: spacetime ripples as a spiral, the chirp signal h(t) runs live, a ring of test masses squeezes. GW150914 as preset, signal to listen to, exaggeration shown.
AstronomyTry it
Hertzsprung–Russell diagram with two stars of equal age: mass decides luminosity, lifetime and fate. Red giant, planetary nebula, supernova, neutron star or black hole; colour computed from temperature.
AstronomyTry it
Space itself stretches: from every galaxy all others recede (switch observer), measure the Hubble diagram yourself, light is stretched and reddened on its way. Time slider from the early universe into the future, a(t) with dark energy.
AstronomyTry it
Two 3D cities from the same random numbers: uniform body heights against a Pareto skyline whose tallest tower pierces the clouds. α slider, running mean, log-log tail, Lorenz curve, the one-in-a-million outlier.
Data & decisionsTry it
The filter invents the relationship: a light wall sweeps through 3,000 independent applicants, the selected fly onto a stage — and there the regression line falls (r ≈ −0.67). Sum, or, and, causal diagram with collider.
Data & decisionsTry it
Number forensics on the first digit: data points land on a glass log drum whose sector width is log₁₀(1+1/d). Rescaling only turns the drum; body height and .99 prices fail, manipulated expenses give themselves away (Nigrini MAD, χ²).
Data & decisionsTry it
Rebuild 2.0 (preview): exact odds via Conway, non-transitivity as a graph on waiting-time rings, waiting-time paradox, matrix of all duels, Monte Carlo, length 3 and 4.
Data & decisionsTry it
Rebuild 2.0 (preview): live headline against reality, population mosaic with case dots, age structure as confounder up to reversal, Farrington's screening method.
Data & decisionsTry it
Rebuild 2.0 (preview): the slide says “A ahead” — opening the look-back morphs the bars into lines and the trend verdict flips. Prior month vs. same month last year, crossings, stock vs. flow.
Data & decisionsTry it
Rebuild 2.0 (preview): five scenarios from abstract to invoice audit, flipped cards land in the truth table, resolution with your own choice pattern and an SQL query.
Data & decisionsTry it
Rebuild 2.0 (preview): covariance as rectangle areas around the centroid, switchable units, least squares as real squares, both regression lines.
Probability & statisticsTry it
Rebuild 2.0 (preview): the same series, every start–end pair as a triangle of returns, distribution of all windows, rebasing to 100 and axis tricks.
Data & decisionsTry it
Rebuild 2.0 (preview): which constant value replaces them all? Returns, speed, savings plan, P/E and semicircle — AM, GM, HM in the replacement test, HM ≤ GM ≤ AM on the number line.
Data & decisionsTry it
Rebuild 2.0 (preview): level of measurement as the set of admissible transformations — five statements hold or flip live, ladder of permitted statistics, sorting exercise with 19 variables.
Data & decisionsTry it
Rebuild 2.0 (preview): the same risk as relative and absolute risk, natural frequency, odds and betting odds.
Data & decisionsTry it
Rebuild 2.0 (preview): St. Petersburg paradox, utility x^γ with certainty equivalent, prospect theory with loss aversion.
Data & decisionsTry it
Rebuild 2.0 (preview): Bayes' theorem with prevalence, sensitivity and specificity, prior and posterior on an absolute scale.
StatisticsTry it
Rebuild 2.0 (preview): location and spread, target parameters n, x̄, s, skewness and kurtosis via sliders.
StatisticsTry it
Rebuild 2.0 (preview): bell curve morphing X → Z with the same area, tail and interval probabilities, inverse quantile question, sampling and a men/women comparison.
Data & decisionsTry it
Rebuild 2.0 (preview): 3D truel with exact survival probability per strategy, Monte Carlo with confidence funnel, selectable turn order and a map of when firing into the air is optimal.
Data & decisionsTry it
Rebuild 2.0 (preview): three real cases — kidney stones, Berkeley 1973, exercise & cholesterol. Subgroups as bubbles, equalise the case mix, and a causal panel asking which view is right.
StatisticsTry it
A conductor's hand with a baton beats 2/4, 3/4, 4/4 and 6/8 while the tip draws a glowing trail in space. The downbeat always comes from above and the baton rebounds from the beat plane, with the melodies of well-known songs lighting up in time. Cue, fermata, cut-off, dynamics and articulation show how the hand shapes music.
Music theoryTry it
A square with two districts whose 60 residents have exactly the same behavioural leanings. The context (library, office, street party, stadium) shifts the norm, control hands out labels, and Becker’s four types separate pure, secret and falsely accused deviants. If one district is checked more often, it carries more labels, and with feedback (exclusion, self-image, scene) it also comes to deviate more over time.
Sociology & networksTry it
A warehouse in four stages: manual, AMR fleet, goods-to-person with cube storage and conveyor, and humanoids in the gaps. The scene rebuilds visibly per stage; metrics show picks per hour, staff, investment, rebuild and flexibility. Humanoids take over the handovers conveyor → AMR and empty totes without a rebuild, but per movement they are slower than people and special systems.
Logistics & Supply ChainTry it
A hub-to-hub route with autonomous Level 4 trucks: in the platoon the following truck saves clearly more fuel than the leader, and the savings grow as the gap shrinks. Roadworks, heavy rain or an exit into the city take the platoon to the edge of its ODD — there autonomy ends with a handover or a minimal risk manoeuvre, and the technical supervisor decides. Plus lead time with and without driving-time rules.
Logistics & Supply ChainTry it
A pod in a partial-vacuum tube, levitating magnetically and driven by a linear motor. Pressure, speed and blockage ratio control the drag live: at high pressure and with a large pod the air piles up ahead of the nose (Kantrowitz limit), and only vacuum and a slim pod make it efficient. In the bend the pod tilts, and if the radius is too tight the lateral acceleration is exceeded. Plus a comparison of energy and travel time with truck, freight rail and air freight.
Logistics & Supply ChainTry it
A palletising cell with infeed, robot, gripper, Euro pallet and outfeed for three case studies: cans, crates and parcels. Kinematics, gripper, stacking pattern, double station and sequencing buffer are selectable; cycle time, capacity against target, pallet change, floor space and feasibility are computed live.
Technical logistics & intralogisticsTry it
A four-station line with yield loss in 3D: utilisation u = λ · t per station, and the bottleneck moves from station 2 to station 4 as yield loss falls. Two live cards show cycle time over utilisation (Kingman/VUT) and Little’s law from a discrete-event simulation, right up to an unstable system.
Technical logistics & intralogisticsTry it
14 continuous conveyors as a 3D exhibition, each with moving goods. Filters for goods, position, accumulation and drive dim the conveyors that do not match, and a jam test shows the difference between accumulating and non-accumulating conveyors. In unit-load mode you pack small load carriers onto a Euro pallet and see the area used.
Technical logistics & intralogisticsTry it
A cruise control drives up the same hill three times: with a fixed pedal, with feed-forward and with feedback control. The plot keeps one comparison curve per strategy, and the block diagram lights up setpoint, controller, actuator, plant, sensor and feedback live. With unknown load or headwind only the closed loop holds the speed.
Technical logistics & intralogisticsTry it
The five basic kinematics in L/O/R/T/V joint notation as 3D industrial robots: gantry (LOO), cylindrical (TLO), polar (TRL), SCARA (VRO) and articulated arm (TRR). Sweeping the joint limits builds the workspace as a point cloud with its hull. A second mode uses a target to show that a robot can be highly repeatable and still inaccurate.
Technical logistics & intralogisticsTry it
A unit-load sorting system like in a parcel hub, from the swap body via weighing, singulation and the scanner tunnel to the chutes. Topology (line, loop, circle), sorter technology (cross-belt, tilt-tray, shoe, pusher) and induction are switchable. A capacity chain shows which area limits the sorting rate: usually induction and identification, rarely the sorter.
Technical logistics & intralogisticsTry it
Example 1 from VDI 5586 in 3D: a tugger train supplies 20 line-side locations on four assembly lines from the supermarket, with coupled or decoupled loading and push or pull (kanban card, e-kanban, call button). Live figures show cycle time, train and driver utilisation, order delay and stock-outs, even while the train still has room.
Technical logistics & intralogisticsTry it
An automated guided vehicle drives the same hall with five navigation methods from VDI 2510: inductive guide wire, magnetic or colour tape, laser with reflectors, dead reckoning with floor markers and SLAM. Put a person in the way or move a station and compare which method keeps going without rebuilding. With safety scanner, error ellipse, lidar map and a VDA 5050 message log.
Technical logistics & intralogisticsTry it
The AGV exercise to work through: loaded and empty trips, handling and waiting add up to the total working time and from it the number of vehicles. Two platforms simulate single transports and accompanying transport side by side; the calculation shows every step with from-to matrix and formulas, plus the break-even processing time.
Technical logistics & intralogisticsTry it
Life-cycle cost analysis of a palletising automation following the lecture’s case study: equivalent headcount, annual cost comparison, net cash flow with the depreciation tax shield, and NPV at the real rate from the Fisher equation. The cumulative discounted cash flow shows the payback period against the logistics threshold of 2–3 years; a positive NPV alone is not enough.
Technical logistics & intralogisticsTry it
Hundreds of floating shards spread in depth join into a motif from one single viewpoint only: WISSEN, RAUM, a cube or an eye. Alignment rises live as you approach the point; sight lines and folding into one image plane show why an image does not reveal depth. Exhibit-ready.
Architecture & scenographyTry it
Chains with weight bags find the shape of pure tension by themselves; inverted they become a stone arch in pure compression, while the semicircle next to it cracks at the marked points. Single arch, a row of arches and the chain net of the Colònia Güell. Exhibit-ready.
Architecture & scenographyTry it
Three tensegrity structures (prism, icosahedron, Snelson's tower), simulated live: the struts never touch, a prestressed cable net holds them. Remove the prestress, add a load or cut a cable, and you see that the stiffness comes from tension. Exhibit-ready.
Architecture & scenographyTry it
An exhibition floor plan that shows on the floor what can be seen from every place and how well it connects to all others. Drag an observer with its view fan, remove walls and send out agents: they walk where integration is high.
Architecture & scenographyTry it
An animal runs through an arena, every spike of a neuron leaves a dot, and a hexagonal grid grows out of random paths. In a concept space of a bird's neck and leg length the same grid appears — the brain orders concepts like places.
Perception & IllusionTry it
Two cube figures: same or mirror images? Response time grows with the rotation angle, and the chart measures your speed of mental rotation in degrees per second. Exhibit-ready.
Perception & IllusionTry it
A 4D cube turns in a chosen plane and is projected into space: in an xw, yw or zw rotation the inner cube seems to turn inside out, although all 32 edges stay equally long in 4D. A true slice with the hyperplane w = c shows what a 3D being would see. Exhibit-ready: also stands on a plinth in "Knowledge as space".
Linear algebraTry it
The triply periodic minimal surface sin x cos y + sin y cos z + sin z cos x = t as a surface with two side colours, as a labyrinth or as a shell: it splits space into two equal, intertwined labyrinths. The level t shifts the surface, volume shares and curvature respond live; cutting it open reveals the channels. Exhibit-ready.
Differential geometryTry it
Horizon and meridian fixed, the celestial sphere turns about the axis tilted to the latitude, the sun runs along the ecliptic. Choose date, time and place: day arc, day length, noon altitude and declination update live — the seasons come from the tilt, not the distance. Exhibit-ready.
AstronomyTry it
The Lorenz equations integrated live as a glowing ribbon: two paths with an initial offset down to 10⁻⁹ drift apart and yet stay on the same double loop. ρ below 24.74 lets the path fall into a fixed point; distance and behaviour are shown. Exhibit-ready.
Chaos & DynamicsTry it
A robot arm with three joints: in forward mode you set the angles and the hand follows; in inverse mode you drag a target and the IK computes the angles — with two, one or no solution at all. Compare PTP and LIN motion on a glue seam, an overhead path and a stretch: the straight line in space turns curved in joint space, and near singularities the joint speed shoots up.
Engineering mechanicsTry it
A 3D production line with five stations shows that the bottleneck alone sets throughput: speeding up other stations only grows inventory and lead time. Drum-buffer-rope ties material release to the bottleneck and lowers inventory at the same throughput.
Logistics & Supply ChainTry it
A live simulation of the reorder point system: safety stock, reorder point and stockouts respond to service level, demand and lead time variability. The curve shows why the last percentage points of service level tie up disproportionate stock and capital.
Logistics & Supply ChainTry it
Four people decide on a team lead, each holding their own info cards. The balance shows why the group makes the worse choice and how asking for unique information in turn changes that.
Data & decisionsTry it
A wheel of fortune gives a random number, then you estimate a question from working life. 200 simulated colleagues show how strongly the number pulls the estimates and what a counterargument does against it.
Data & decisionsTry it
A sales team across two quarters: the best fall back and the weakest catch up without anyone changing anything. A slider for the share of luck shows when this happens and how strongly.
Data & decisionsTry it
One workforce, many surveys: see how far results jump with few answers and why it takes four times as many answers to halve the uncertainty.
Data & decisionsTry it
An AI answer sounds certain and cites sources. Break it into claims and check each against the original document: supported, refuted or made up.
AI literacyTry it
A model trained on past hiring decisions sorts 200 applications. Delete the group from the data and the ratio barely improves, because a proxy feature carries the bias on.
AI literacyTry it
Aperture, shutter and ISO on a simulated photo: a park scene with a passing coupé and string lights, by day, at dusk or at night. A wide aperture softens the background and enlarges the bokeh, long shutter speeds smear the car into light trails, high ISO adds noise. "Hold EV" balances every change with another setting — light balance in stops, light meter and live histogram show: same brightness, different look.
School physicsTry it
A 3D cell divides: interphase to cytokinesis on a scrubbable timeline, with counters for chromosomes, chromatids and DNA content. It shows why both daughter cells receive the same chromosome set.
Biology (Gymnasium)Try it
One diploid cell becomes four different gametes: follow in 3D how meiosis I separates homologous chromosomes and meiosis II sister chromatids. With crossing over, a shuffle for random assortment, n/2n and DNA counters, and nondisjunction leading to trisomy 21.
Biology (Gymnasium)Try it
The Meselson–Stahl experiment as a 3D lab story: from the ¹⁵N culture through the ultracentrifuge to the UV image of the bands. Compare the predictions of conservative, semiconservative and dispersive replication with the measurement and find out which generation refutes which hypothesis.
Biology (Gymnasium)Try it
An RNA polymerase reads a gene in 3D: the bubble travels along and the mRNA grows 5′→3′ on the template strand. For eukaryotes with cap, poly-A, splicing (lariat, alternative splicing) and export through the nuclear pore; enter your own DNA sequence.
Biology (Gymnasium)Try it
A ribosome reads the mRNA codon by codon: charged tRNAs act as adapters and deliver their amino acid to the A site, the rRNA forms the peptide bond, until a stop codon releases the protein. Change bases or the reading frame and watch the protein change live, up to a polysome.
Biology (Gymnasium)Try it
Tap a base in the real β-globin gene and watch the mRNA and amino acid chain rearrange: silent, missense, nonsense or frameshift. Plus the sickle cell, chromosome and genome mutations, and UV damage with repair.
Biology (Gymnasium)Try it
Zoom from the chromosome via the nucleosome to the double helix and a single nucleotide, with a true scale bar. Tap base pairs, unwind and open the helix, show grooves and dimensions, and watch the antiparallel complementary strand form for a sequence you type.
Biology (Gymnasium)Try it
One DNA becomes two: replication bubbles open at many origins and merge while an enzyme team builds the new strands at every fork. Old strands stay visible in colour, and the Meselson-Stahl comparison shows why replication is semiconservative.
Biology (Gymnasium)Try it
Close-up of a replication fork in 3D: both polymerases work only 5′→3′, so the leading strand grows in one piece and the lagging strand in Okazaki fragments. The trombone model in motion, with primer replacement, a ligase switch and a bacterium/eukaryote comparison.
Biology (Gymnasium)Try it
A human body cell at 1 unit = 1 µm: nucleus with double envelope, nuclear pores and chromatin, rough ER continuous with the nuclear envelope, smooth ER, Golgi (cis/trans), endosomes, lysosomes, peroxisomes, mitochondria with cristae and mtDNA, centrosome, microtubules, actin cortex and intermediate filaments. The secretory pathway in seven scrubbable phases: transcription, nuclear pore, translation at the rER, COPII to the Golgi, cis→trans, vesicle on a microtubule, exocytosis. Cutting plane, layers and a membrane loupe.
Biology & neuroscienceTry it
A neuron from the dendrites to the synapse: EPSPs sum at the axon hillock, above threshold an action potential arises and jumps from node to node at full strength. Loupes show Na⁺/K⁺ channels with inactivation and the Na⁺/K⁺ pump at a node of Ranvier, and Ca²⁺ influx, vesicle fusion and receptors at the synapse. Eight scrubbable phases with a potential trace, a subthreshold stimulus and myelin on/off for comparison.
Biology & neuroscienceTry it
A saguaro in the Sonoran Desert over 24 hours: at night the stomata open and CO₂ is stored as malic acid in the vacuole; by day they stay shut and the Calvin cycle turns it into sugar. Cell zoom, acid curve and a water counter compared with a C3 plant.
Biology & neuroscienceTry it
Every new areole forms at the apex, turned by the same angle against the previous one. At the golden angle of 137.5° the cactus shows 8, 13 and 21 spirals; half a degree off, the pattern breaks into arms with gaps, and at 144° into five straight spokes. Change the angle live, watch it grow, colour and count the spirals.
Biology & neuroscienceTry it
What heyprof is, in one circle: teachers add material to the course, the AI tutor learns from it, learners ask and explore, and feedback flows back. Four areas to try: drag material onto the course, ask the tutor and find the aha in a mini app, open a learner’s progress, vote in the live quiz.
heyprofTry it
Plato's allegory of the cave as a walkable 3D cave: from a prisoner's first-person view the shadows on the wall are the whole world; only the cross-section reveals fire, low wall and carriers. Seven stations lead from turning around through the ascent to the sun and back into the dark, with the eyes dazzled and adjusting. The four levels of the divided line and quotes with Stephanus references complete the picture.
PhilosophyTry it
Ebbinghaus’ original data from 1885 and a teaching model of the forgetting curve as ribbons over a time axis. Two study plans with the same effort compared: cramming the day before versus spaced reviews, read off on exam day and one week later. Plus a self-test with nonsense syllables.
PsychologyTry it
The iterated prisoner's dilemma in three views: an Axelrod tournament with nine strategies and a builder for your own, the evolution of population shares over generations, and a spatial grid after Nowak & May where cooperators and defectors can be painted in. Tit for Tat wins the tournament without winning a single match; on the grid, cooperators hold out in groups.
Sociology & networksTry it
A 3D city of two groups on a grid with vacant lots. Anyone with fewer like neighbours than the tolerance threshold requires moves to the nearest suitable vacant lot. Metrics and a chart show that even at a threshold of one third the share of like neighbours rises from about 50 % to about 70 %.
Sociology & networksTry it
The character network of a play in 3D: characters are linked when they speak in the same scene. A timeline builds the network scene by scene. Share of speech and centrality (degree, betweenness) side by side, with DraCor data for Faust I, Intrigue and Love, Emilia Galotti and Mary Stuart.
LiteratureTry it
Lines of classic German poems as waves of stressed and unstressed syllables. Foot schemes can be laid over the lines; the app marks where a scheme violates word stress. A beat track, read-aloud and tap-along make metre, line endings and rhythm audible, with rhyme shown separately.
LiteratureTry it
How Egyptian picture signs became the Latin alphabet via Proto-Sinaitic, Phoenician and Greek forms. Each letter A–Z morphs on an engraved tablet through eight stages, with direction of writing, map, comparison and word test. Uncertain derivations are marked as conjectured.
Linguistics & phoneticsTry it
In time-lapse, a river winds across a flat floodplain. The cut bank is eroded and a sandbar grows on the point bar until a cutoff severs a loop and leaves an oxbow lake behind. Cross-profile with secondary flow, erodibility, valley slope and bank protection are adjustable.
Geography & earth scienceTry it
Spatial family tree of the Indo-European languages, with height showing time from Proto-Indo-European to today. Ten basic words travel from the reconstructed root to about 30 languages; the First and Second Sound Shift and the centum/satem split are marked in colour in the forms. A test separates true cognates from chance look-alikes and loanwords.
Linguistics & phoneticsTry it
Four illusions that only work from a single viewpoint, as walk-around 3D stations: Ames room (giant and dwarf; the people swap corners), Penrose triangle as a real object with a gap, Beuchet chair and a rotating hollow mask with switchable lighting. A viewpoint slider moves from the peephole to the outside view. True shape, lines of sight and readouts show why the brain picks the most probable interpretation of an ambiguous retinal image.
Perception & IllusionTry it
The Hell of Dante's Commedia as a funnel beneath Jerusalem, cut open down to the centre of the Earth. Dante and Virgil descend through the vestibule and nine circles; for each circle the app shows sin, punishment (contrapasso), figures and canto. A diagram orders the circles after Inf. XI: incontinence, violence, fraud.
LiteratureTry it
Symphony orchestra on the concert stage with all instrument families, in German and American seating. A timeline following the plan of Ravel's Boléro shows how the crescendo grows from more and more instruments. The same note on different instruments makes the overtone spectrum and the attack visible as the basis of timbre.
Music (Gymnasium)Try it
Three self-experiments on selective attention: a spot-the-change task in the flicker paradigm, a counting task with an unexpected object and a letter stream showing the attentional blink. Own measurements (time to detection, noticed yes/no, hit rate per gap) appear next to literature values. Procedural 3D scenes, results stay local in the browser.
PsychologyTry it
Alberti's window in 3D: sight lines from the eye point pierce a glass pane and draw a Renaissance hall line by line as a perspective image. Eye height, sideways position and the distance of the picture plane are adjustable; a rotatable cube shows two vanishing points. Finally the camera moves into the eye point: image and space match exactly, then only the flat panel remains.
ArtTry it
Section through four bays of a basilica in 3D: a slider moves from the Romanesque with round arches and thick walls to the High Gothic with pointed arches, flying buttresses and pinnacles, while the windows open up and the light inside increases. The thrust line in the section shows whether the thrust stays within the middle third of wall and buttress. Without the flying buttress it leaves the Gothic wall, the wall tips over and the vault collapses.
Architecture & scenographyTry it
Five tiles of equal edge length carry strap lines that cross every edge at its midpoint at 54° and therefore continue across every tile boundary. A decagon is constructed with compass and straightedge, tiles can be placed and hidden. A periodic pattern is compared with a Penrose subdivision that has tenfold symmetry without repetition.
ArtTry it
A Japanese colour woodblock print after Hokusai's "Great Wave" is built up pass by pass: key block first, then a separate mirror-inverted block for each colour, inked, laid against the registration marks (kentō) and rubbed with the baren. Layers can be switched off one by one, the registration marks removed and the stack of blocks and colour layers opened. The picture only exists in the stack; each block carries a single colour.
ArtTry it
A park painting made of tens of thousands of pure colour dots in the spirit of Seurat's Grande Jatte. As the distance grows, the dots merge once each appears at less than about one arcminute. A comparison field shows that blue next to yellow turns light grey from afar, while mixed on the palette it turns green. Your own photos can be pointillised locally.
ArtTry it
Two figures in conversation, three film cameras and the line of action as a café scene in 3D. The camera images appear live as a film strip: if a camera stands across the axis, both figures look in the same direction across the cut. With shot sizes, a move across the axis and a neutral shot.
Film & mediaTry it
A film scene at dusk is graded live: looks such as teal & orange, bleach bypass or day for night, colour wheels for shadows, midtones and highlights, tone curve and saturation. A vectorscope with skin tone line and a before/after wipe show that a look shifts colours by brightness range, while a simple colour filter tints everything alike.
Film & mediaTry it
Toroidal field, tokamak and stellarator compared: without twisted field lines, ions and electrons drift apart and the plasma drifts onto the wall. The stellarator achieves the twist with 50 bent coils alone, without a current in the plasma. Field lines, particle orbits (Boris pusher), Poincaré section with magnetic islands and triple product.
PhysicsTry it
How an EUV scanner exposes chips: tin plasma, collector, facet mirrors, a reflective mask and six projection mirrors image the pattern onto the wafer, reduced 4 : 1. Slow motion of the source, the power loss over 10 mirrors and a computed aerial image show why 13.5 nm allows finer features than DUV.
Devices & operating manualsTry it
The Atlantic overturning circulation on a 3D globe: more freshwater weakens it until it tips, and turning back alone does not restore it. Stommel box model with hysteresis, meridional section and temperature effects for Europe.
Geography & earth scienceTry itArchive
A mechanical watch movement to take apart: balance wheel and hairspring set the beat, the Swiss lever escapement releases the mainspring energy in portions. Escapement cycle in slow motion and steps, spring tension and amplitude, gear ratios with proof.
Physics experiments (Deutsches Museum)Try it
Cornering, ice and a locked differential on a rear axle: the spider gears let the wheel speeds differ, n_L + n_R = 2 · n_carrier, and split the torque equally. On ice one wheel spins until the lock is engaged.
Automotive engineeringTry it
A real protein chain folds before your eyes: hydrophobic collapse, helices and sheets, energy funnel and Levinthal calculation. Heating unfolds it, cooling folds it again.
Biology & neuroscienceTry it
The cochlea uncoils: a travelling wave runs along the basilar membrane and peaks at its Greenwood place – high tones at the base, low tones at the apex. Two tones give two peaks, the microphone shows your own voice as a pattern; cross-section with the organ of Corti, age-related hearing loss and noise damage.
Biology & neuroscienceTry it
22 cars on a ring road: above a critical density a brief braking turns into a jam wave that travels backwards. Space-time and fundamental diagrams show why tailgating lowers the flow and why a few ACC cars smooth out the waves.
Logistics & Supply ChainTry it
Thousands of particles flow step by step from Gaussian noise into shapes: forward and reverse process, DDPM vs. DDIM and classifier-free guidance. An image panel shows the same in pixel space, coarse shape first and details last.
Neural networksTry it
Real-time ray tracing of a Schwarzschild black hole: the far side of the accretion disk appears as an arc above the shadow, and the shadow is 2.6 times the size of the horizon. With a no-curvature comparison, masses from 10 M☉ to M87*, and a falling probe that freezes at the horizon.
AstronomyTry it
Both eyes from BodyParts3D with six eye muscles, trochlea, optic nerve and visual pathway. Drag the gaze target and see which muscle works; CN III, IV or VI palsy with double vision. In the section a real ray path: cornea and lens refract, the lens accommodates with age, short- and long-sightedness with matching glasses.
Biology & neuroscienceTry it
A BodyParts3D skeleton with 64 leg muscles walks on a treadmill, driven by averaged gait-lab measurements of about 50 adults at five walking speeds. Scrub the gait phases, joint angles with spread, EMG of eight muscles colouring the muscles in the model, ground reaction force as an arrow at the centre of pressure.
Biology & neuroscienceTry it
Vier aktuelle Geräte (iPhone 17 Pro, Pixel 10, Galaxy S26 Ultra, Fairphone 6) maßstäblich nach den iFixit-Teardowns 2025/26: Explosions-Slider fährt Display, Rahmen, Akku, Logic Board, Kameras, Spule und Rückseite auseinander, jedes Bauteil klickbar mit Funktion und Modellbesonderheit (Akku-Tray mit 14 Schrauben, Pull-Jacket, verklebtes Privacy-Display, 12 Module). Röntgenblick und Vergleich: Akku ist das größte Teil, der Rechner ein Daumennagel — und Reparierbarkeit ist eine Konstruktionsentscheidung.
Devices & operating manualsTry it
An anatomical heart with 95 parts: anatomy, cardiac valves, circulation and electrical activation with ECG. Slow motion, transparent walls, disassembly and five simplified condition comparisons connect electrical signals, contraction and blood flow.
Biology & neuroscienceTry it
Explore a personal AI agent as a blueprint: channels, gateway, memory, skills, tools, models, browser and sandbox. Six scenarios trace a message through the system.
AI literacyTry it
Ein Kübel Wasser am Seil über Kopf geschwungen: Drehzahl und Seillänge einstellen, Kraftpfeile am Scheitel beobachten. Bleibt v² ≥ g·r, drückt der Boden das Wasser nach innen; darunter wird die Bodenkraft null und das Wasser kippt in Zeitlupe heraus — ganz ohne „Fliehkraft".
PhysicsTry it
Ein echter Einzylinder-Viertakter (68 × 45 mm, 163 cm³, OHV) maßstäblich als Schnitt- und Explosionsmodell: Kurbelwinkel 0–720° drehen, Kolben, Pleuel, Kurbelwelle, Nockenwelle mit 2:1-Zahnrädern, Stoßstangen, Kipphebel und Ventile arbeiten sehen; Gas färbt sich je Takt, Zündung vor OT, Ventilüberschneidung sichtbar, p-V-Diagramm läuft mit.
Automotive engineeringTry it
Schub als Impulsstrom, Widerstand quadratisch: m·dv/dt = ṁ·v_e − ṁ_a·v − k·v². Vier Presets (Übungsaufgabe, Kampfjet, Verkehrsflugzeug, Business-Jet), alle Größen als Slider; Kurven v(t) und a(t) mit v_max-Linie und Zeit bis 99 %, dazu die geschlossene Lösung Schritt für Schritt.
Engineering mechanicsTry it
Wasserhahn mit glasklarem Strahl: Durchfluss und Mündungsdurchmesser steuern die Reynolds-Zahl. Laminar steht die Form still, obwohl Farbstoff-Tracer mit Metern pro Sekunde hindurchfließen; im Übergang kräuselt sich die Oberfläche, turbulent zerfällt der Strahl in Tropfen. Ein Finger im Strahl zeigt, wie empfindlich die Ordnung ist.
PhysicsTry itWant to use these apps in your courses, or have an idea for a new one? Let’s find out what works for you.
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