Labs

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Primary

Coins
19 rooms · Slide coins to turn one figure into another.
Primary Logic Puzzles
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Trios Lab
22 rooms · Learn to identify valid trios step by step.
Primary Combinatorics
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Euler's walk
23 rooms · Drawing without lifting the pencil: the magic rule of Eulerian graphs.
Primary Graphs
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Mazes
20 rooms · Walk through famous mazes around the world and learn the tricks to never get lost: right-hand rule, Tarry and Trémaux.
Primary Mazes Graphs Algorithms
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Symmetry Lab
22 rooms · Explore axial symmetry and create mandalas
Primary Symmetry Geometry
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12 25 17 14 18 18 6 30 7 24 5 13 11 23 42 🐰 🥕
Number mazes
16 rooms · Cross mazes stepping only on multiples of a number, and later by solving operations along the way.
Primary Mazes Operations
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Polyominoes
23 rooms · Dominoes, trominoes, tetrominoes and pentominoes: cover shapes, prove things with colorings, count ways to fit pieces, and design your own challenge for a classmate.
Primary Combinatorics Logic Polyominoes
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Visual patterns
21 rooms · Work out the next steps of a visual series and check it yourself.
Primary Logic Patterns
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Colouring
18 rooms · Paint squares, triangles, numbers and countries by the rules: no two neighbours alike, two of a kind in every square, the product of two colours gets the third. Colour maps with just four colours and discover how a good colouring proves that some things are impossible.
Primary Logic Combinatorics
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Secondary

? + 3 = 15
Equations · The hidden number
15 rooms · Guess the number I am thinking of. Learn to read linear equations and undo operations to solve them.
Secondary Equations Algebra
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Powers, exponentials and logarithms
22 rooms · From counting factors to graphing curves: the properties of powers, the exponential function that always ends up winning, and the logarithm as its inverse question.
Secondary Powers Functions
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x 1 corte
Polynomial and rational functions
19 rooms · From lines to hyperbolas: graphs, domain, range and how each parameter changes them.
Secondary Functions
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la edad de mi padre es... x + 2 🧒 👨 x x + 2
Equations · From the story to the equation
13 rooms · Learn to translate a word problem into an equation. Variables, expressions and the key equality that leads to the answer.
Secondary Equations Word problems
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x y
Linear functions
12 rooms · Lines y = m·x + n. Slope, intercept and graph recognition.
Secondary Functions
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Lines that form curves
15 rooms · When many lines touch each other, they trace parabolas, hyperbolas, cardioids, astroids…
Secondary Curves
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Brachistochrone: the fastest curve
9 rooms · Discover why the fastest curve is not the shortest.
Secondary Curves
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Epidemic
17 rooms · How a disease spreads: from the simple SIR model to real COVID data. Along the way, cellular automata, vaccines, lockdowns and social networks.
Secondary Biology Graphs Percolation Cellular automata
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A B C D E F G H D E F G H I J K
Cipher zoo
17 rooms · Six historical ciphers for hiding messages: from the reversed Hebrew alphabet to the American telegraphers' zigzag. Ends with 3 camp cryptographer missions.
Secondary Cryptography
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The catenary
8 rooms · The hanging chain, bridges and Gaudí's arches.
Secondary Curves Architecture
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Order from chaos
23 rooms · Four completely different mechanisms of the same principle: with only simple local rules, random noise spontaneously reorganizes into patterns. Spirals, flocks, sync, fractals.
Secondary Chaos Cellular automata Modelling
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Ageing
8 rooms · Gompertz, cells and mitochondria: the mathematics of ageing.
Secondary Aging Biology Modelling
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Propagation
14 rooms · How something spreads — a rumour, a virus, a wildfire — through a network or a map: links, hubs, and the famous threshold.
Secondary Graphs Percolation Cellular automata
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Weather & Climate
8 rooms · Pressure, wind, rain and hurricanes: control the Iberian Peninsula's weather with real physics.
Secondary Climate Geography Modelling
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5 10 ?
Exchanges and invariants
19 rooms · Can you get from here to there? If not — what stops you?
Secondary Invariants Modular arithmetic
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↻
Phantom traffic jams
13 rooms · A traffic jam can appear with no crash, roadworks or traffic light. Find out why.
Secondary Chaos Modelling Cellular automata Upper secondary
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High school

Function analysis
21 rooms · From function families to their full graphical analysis: domain, extrema, limits and discontinuities, with zoom to see them up close.
High school Calculus Functions
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Circular Trigonometry
25 rooms · Sine and cosine are born from a point going round a circle. From the unit circle to sound waves, ellipses, the double angle and polar coordinates — and along the way, how a computer draws a circle.
High school Trigonometry Functions Geometry
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x y
The derivative
32 rooms · From visual intuition to calculation: slopes, limits, numerical differentiation and rules.
High school Calculus Functions
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4D
The fourth dimension
17 rooms · Regular polyhedra exist in 4D: tesseract, hexadecachoron, icositetrachoron… Rotate their 3D shadows to imagine what they look like.
High school Geometry Fourth dimension
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conejos zorros
Population Models
17 rooms · Foxes, rabbits and equations that pulse. From individual agents to three-species chaos: why populations oscillate and what they share with the three-body problem.
High school Differential equations Biology Modelling
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Train your network
7 rooms · Design a spaceship's sensors and train it by playing: your moves become training examples for a neural network that learns to dodge bombs and collect stars.
High school AI Neural networks Upper secondary
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1 0 1 1 0 1 H · log₂
Information
22 rooms · How information is measured, encoded and protected from noise. Hartley, Shannon, Hamming.
High school Information Codes
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Chaos
10 rooms · Deterministic systems you still cannot predict.
High school Chaos Physics
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Axelrod's tournament
16 rooms · Why does cooperation emerge among selfish players? From the one-shot prisoner's dilemma to a tournament of strategies, to the evolution that rewards the best scorers. Rebuild Axelrod's experiment and discover why winning every duel is not winning the tournament.
High school Game theory AI
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Turing patterns
12 rooms · Turing and Gray-Scott reaction-diffusion. Spots, stripes and mazes emerge from two substances that diffuse and react. Design the pattern of your own animal.
High school Modelling Biology
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★
Training the AI to play
20 rooms · How does a machine learn to play with nobody teaching it the strategy? Boxes of beads that reward and punish moves discover perfect play on their own — from the stone game to Hexapawn to a teamwork game with no single solution.
High school AI
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function setup () {'{}'} createCanvas background (30) } function draw () { fill ( 255 ,0,0) circle (mouseX, mouseY, 30) }
Create with p5.js
35 rooms · Learn to program animations and interactive images with p5.js. From your first shape to your own functions, all with live code and result.
High school Programming
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Curved worlds
24 rooms · The geometry you learned is not the only one: it depends on the shape of space. Measure triangles on the plane, the sphere and the hyperbolic world to discover three different geometries.
High school Geometry
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f : A → B
Functions: concept, domain and range
16 rooms · What is (and isn't) a function, injective/surjective/bijective, and how to find the domain of a real function.
High school Functions
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x y
Linear optimization
17 rooms · Getting the most out of limited resources: from the word problem to the model, from the model to the picture, and from the picture to the simplex method and the dual problem.
High school Optimization Linear algebra
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OR
Logic
24 rooms · Circuits, truth and lies, sets: learn the logic operators by building them.
High school Logic
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Infinity
24 rooms · Sheep, impossible hotels and a vase that empties itself: a journey through infinity, from the classic paradoxes to the different sizes of infinity and the strange Cantor set.
High school Logic Set theory
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University

☀️ ☁️ ☔ 🐸
Markov chains
20 rooms · Predicting the weather, Bitcoin, your next word, and which web pages matter — all with one idea: tomorrow depends only on today.
University Probability Modelling
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y
Neural Networks
29 rooms · Build, train and watch artificial neurons: weights, sigmoid, gradient descent, backprop. No manual calculation — everything is automatic, you design.
University Neural networks AI
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A B C D E D E F G H +3 RSA
RSA Cryptography
27 rooms · Learn the RSA algorithm step by step: Caesar cipher, modular arithmetic and Euler's φ function.
University Cryptography Modular arithmetic
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x y
Function interpolation
29 rooms · Approximate unknown values from known data: from the tangent line to Lagrange, Newton, Taylor and cubic splines.
University Calculus Functions Numerical analysis
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1
The simplex method
23 rooms · Solving linear optimization problems without drawing them: standard form, the simplex tableau, walking the vertices and the dual problem.
University Optimization Linear algebra
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Heuristic optimization
35 rooms · Looking for the minimum of a function you cannot see and can only query point by point: from pure randomness to annealing, swarms and genetics, all compared on the same budget.
University Optimization Algorithms
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x y
Definite integrals and areas
18 rooms · From counting grid squares to Riemann sums and the definite integral, with applications to areas, arc length and volumes.
University Calculus
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2ε 2δ
Continuity: ε, δ and topology
21 rooms · The ε-δ definition played as a duel, metrics that change the verdict, sequences, and the moment continuity stops needing distances.
University Topology Calculus Functions
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P Q P + Q
Elliptic curves
26 rooms · A line meets the curve y² = x³ + ax + b in three points: from two of them you build the third. Drag points, add with chords and tangents, multiply a point by n and hunt rational points like Diophantus and Bachet. Discover torsion, the points that come back to the start, and Mazur’s theorem, which allows only 15 shapes. Finally, the same curve in modular arithmetic: multiplying is lightning fast and undoing the multiplication is almost impossible. The cryptography that protects the internet rests on that.
University Number theory Algebra Cryptography
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a x⁵ − x + a
The quintic with no formula
27 rooms · Move a coefficient of x⁵ − x + a around a loop and the five roots come back to their places… but in a different order. With this idea of V. I. Arnold one proves that the quintic has no formula in radicals: loops, permutations, commutators and the group A₅, which never lets itself be reduced. Special rooms to pick your own polynomial, see its branch points, draw your own loops and compute its monodromy group. Follows lecture 5 of “Mathematical Omnibus” (Fuchs and Tabachnikov) and the book by V. B. Alekseev.
University Group theory Equations Topology Algebra
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