Playground

Uniform random points are scattered across the unit square. The fraction landing inside the quarter-circle (where x² + y² ≤ 1) approaches π/4, so π ≈ 4 · inside / total. Every number shown is derived from the running counts — nothing is precomputed. Error shrinks on the order of 1/√N, which is why the estimate settles slowly on the log-scaled convergence chart.

A small multilayer perceptron is trained from scratch with real forward propagation and backpropagation (per-sample stochastic gradient descent, a sigmoid output, and binary cross-entropy loss). The shaded field is the network's current prediction over the plane — it is re-sampled every training batch, so the decision boundary visibly bends to fit the data as loss falls. Try switching the dataset to XOR with a single hidden layer to watch it struggle, then add a layer.

Each algorithm is implemented as a generator that yields a step — compare, swap, or overwrite — for every operation it performs, and the visualization advances those steps frame by frame. The bars are the live array; highlighted bars are the indices being touched right now. The comparison and swap counts are the algorithm's actual work, and the complexity figures come from the selected algorithm's metadata.