See important AI algorithms come alive and experiment with them: a genetic algorithm that evolves a solution to the N-Queens puzzle generation by generation, an algorithm that uncovers hidden groups in a social network, search algorithms that find their way out of a maze, and chess against an AI that thinks with adversarial search (minimax and alpha-beta) and shows you its thoughts. Everything runs in your browser.
Best fitness Population average Goal
A genetic algorithm imitates natural evolution: it starts from a population of random solutions, selects the fittest, combines them (crossover), changes them slightly at random (mutation), and repeats generation after generation. In the N-Queens puzzle, N queens must be placed on an N×N board so that no two attack each other. An individual's fitness is the number of queen pairs that do not attack each other; red lines show the attacks that remain.
This is the classic example from Russell & Norvig, the textbook of my AI course. Try a mutation rate of zero: the population can lose its diversity and get stuck just short of a solution. AI course materials
Drag nodes to rearrange the network
In social networks, some groups of people interact far more with each other than with everyone else — these groups are communities. This network has hidden communities, and the label propagation algorithm tries to discover them with no prior knowledge: every node repeatedly adopts the label most common among its neighbours.
Quality is measured with modularity and normalised mutual information (NMI) — the same measures I used to evaluate a hybrid metaheuristic for community detection (2025). Raise the mixing μ and the boundaries blur, making the task harder. Read the paper
Drag to draw walls · drag ● start or ★ goal to move them
| Algorithm | Explored | Path |
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Search algorithms are a cornerstone of AI. BFS guarantees the shortest path but explores widely; DFS dives ahead but its path is not necessarily short; Greedy looks only at the distance to the goal; A* combines the cost so far with an estimate of the remaining distance, so it is both optimal and efficient. Run several algorithms on the same grid and compare. AI course materials
Expanded at each depthFrom the goal (bidirectional)
| Algorithm | Expanded | Frontier | Moves | s |
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Uninformed (blind) search knows nothing about how far a state is from the goal: it can only tell the goal when it sees it, and the algorithms differ only in the order they expand nodes. Breadth-first goes layer by layer and finds the shortest solution, but its frontier grows like b^d. Depth-first dives down one branch: very little memory, but its solution can be absurdly long. Depth-limited search stops at a fixed depth; iterative deepening tries limits 0, 1, 2 … and gets the best of both — the shortest solution with the memory of depth-first — at the price of re-expanding the shallow levels (see the chart). Uniform-cost search expands the cheapest path first and stays optimal when moves cost different amounts. Bidirectional search runs from both ends and meets in the middle: about 2·b^(d/2) nodes instead of b^d.
The 8-puzzle has 9!/2 = 181,440 reachable states; the other half can never be reached, because a move never changes the parity of inversions. Press “Make it unsolvable” and see which algorithms can tell there is no solution (completeness). Compare with A* in the “Search Algorithms” tab, which uses a heuristic. AI course materials
You are reviewing an earlier position — press ⏭ to return to the game.
Players
Your pieces (starts a new game)
Moves
Evaluation over the game
Principal variation (the line it expects)
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Candidate moves at the root
Values are in pawns from the side to move. “≤” means alpha-beta proved the move is no better than that and stopped looking — that is pruning. Gold arrow: its current best move; blue: the moves it expects next.
Search algorithm
Evaluation function
For the position on the board: every move of the side to move (MAX) and the opponent's replies (MIN). MIN takes the reply worst for MAX; MAX takes the move whose worst case is best. Alpha-beta stops looking at a move as soon as one reply shows it cannot beat a move already found.
All three search the same position to the same depth. Alpha-beta always returns the minimax value — it only skips branches that cannot matter. How many positions does each one need?
| Algorithm | Positions | Seconds | Move |
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Chess is a two-player, zero-sum game with perfect information: what one side gains, the other loses, and both see everything. Von Neumann's minimax theorem (1928) says such a game has a value: MAX maximises the outcome assuming MIN replies with the move that minimises it. The minimax algorithm computes it by searching the game tree; since about 35 moves are possible in a typical position, the tree grows as 35^d and no computer can search it to the end.
…stops at a fixed depth and estimates the position with a heuristic evaluation function (material, piece placement, king safety); prunes with alpha-beta, which with perfect move ordering searches about 35^(d/2) positions instead of 35^d and so reaches twice the depth in the same time; deepens iteratively and remembers positions it has already seen (transposition table); and keeps searching captures past the horizon (quiescence) so it does not stop in the middle of an exchange. The “deliberate error” slider weakens it like a human of bounded rationality: a fixed random error in every evaluation. AI course materials
Click to add a point · Shift-click or right-click for the other class
Each neuron computes a weighted sum of its inputs and passes it through an activation function (tanh in the hidden layers, the sigmoid at the output, which gives the probability of the blue class). Learning means adjusting the weights to reduce the error: backpropagation computes how much each weight is to blame, layer by layer from the output back, and gradient descent moves it a little the other way.
Try the perceptron on XOR: a single neuron draws only a straight line, so it fails — the observation (Minsky and Papert, 1969) that hidden layers answer. Too high a learning rate makes the error jump around; too low, and learning crawls. AI course materials
Click a cell: empty → wall → trap
Nobody tells the agent where the goal is: it only gets a reward (+10 at the goal, −10 in a trap, a small cost for every step) and keeps, for every cell and move, an estimate Q of the total reward to come. After each move it nudges that estimate: Q(s,a) ← Q(s,a) + α[r + γ·max Q(s′) − Q(s,a)]. The goal's reward spreads back cell by cell, and the arrows come to point the way.
ε is the explore-or-exploit dilemma: with ε = 0 the agent repeats what it knows and may never find a better way; with ε = 1 it only wanders. γ is patience: how much a reward later is worth now. AI course materials
Click to add points
| K | SSE | Drop |
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K-means needs no labels (unsupervised learning). It repeats two steps: assign every point to its nearest centre, then move every centre to the mean of its points. Each round lowers the sum of squared distances (SSE), so it always stops — but perhaps in a local minimum, which is why the start matters: k-means++ picks centres far from each other.
Try “two rings”: K-means looks for round, compact groups and cuts the rings in half. The elbow table helps choose K: where one more cluster stops lowering the error much. AI course materials
