Spotlight #1 — Math & Algorithms

From sorting algorithms you can watch race each other to geodesic domes you can build in three clicks — the Math & Algorithms category is one of the richest on the site. Here's what's in it and where to start.

11
simulations
3
difficulty levels
4
sub-areas

Mathematics is the language of every simulation on this site, but the Math & Algorithms category puts the maths itself front-and-centre. The focus is on visual intuition — seeing why Euclid's algorithm converges, watching A* navigate a maze, or rotating a geodesic dome to understand its structure.

All 11 Simulations

📊
Sorting Algorithms
Race Bubble Sort, Merge Sort, Quick Sort and Heap Sort side by side. Watch comparisons and swaps in real time.
Canvas 2DEasyPopular
🌀
Maze Generator & Solver
Generate perfect mazes with DFS and Wilson's algorithm, then solve with BFS, DFS or A*. Visualise the search frontier.
Canvas 2DModerate
🗺️
Travelling Salesman
Compare nearest-neighbour, 2-opt, and simulated annealing on up to 50 cities. Watch cost improve in real time.
Canvas 2DAdvanced
🔺
Sierpiński & Fractals
Chaos game, L-systems, and recursive triangle — six classic IFS fractals with zoom and depth controls.
Canvas 2DEasy
🌀
Number Spirals
Ulam spiral, Sacks spiral, and prime gaps visualised on polar and Cartesian grids. Patterns in the primes appear immediately.
Canvas 2DEasy
🌿
Barnsley Fern
Iterated Function System that renders a photorealistic fern from four affine transforms. Tweak coefficients to deform the fern.
Canvas 2DEasyNew
🔷
Voronoi Diagrams
Fortune's sweep-line algorithm builds the diagram in O(n log n). Drag seeds to reshape regions; toggle Delaunay triangulation.
Canvas 2DModerate
🟦
Cellular Automata
1D and 2D CAs: Wolfram elementary rules, Game of Life, Forest Fire, Brian's Brain. Rule editor included.
Canvas 2DEasyPopular
🎲
Random Walk
1D and 2D random walks, Lévy flight, self-avoiding walk. Compares path statistics (variance, MSD) live.
Canvas 2DEasy
🔮
Geodesic Domes
Icosahedron subdivision frequencies 1V–5V. Analyse vertex/face/edge counts via Euler's formula F = f²×20, V = F/2+2.
Three.jsModerate
🌐
Spherical Projections
Five map projections compared side by side with Tissot indicatrices. See how each distorts area, shape and distance.
Canvas 2DModerate

Where to Start

If you're new to the category, start with Sorting Algorithms — it's the most instantly understandable and often the best hook for students who've heard of bubble sort but never seen it lose.

If you're comfortable with discrete maths, go to Travelling Salesman next. Watching 2-opt improve a greedy tour over hundreds of iterations is a better explanation of local search than any textbook diagram.

For geometry and visual maths, Geodesic Domes and Spherical Projections are the most visually striking. The spherical projections demo was built specifically for geography and cartography courses.

Behind the Algorithms

Most of the Math category uses plain Canvas 2D — the algorithms are the work; the renderer just needs to get out of the way quickly. The two Three.js exceptions are Geodesic Domes (genuine 3D geometry) and a forthcoming 4D hypercube demo.

Up next in Spotlight #2: the Quantum Physics & Quantum Computing categories — Bloch spheres, Bell states, and Grover's algorithm in your browser.