WING V · AUTOMATA
A computer is not a machine that calculates. It is a machine that follows a rule with no idea what the rule is for. Every exhibit in this wing is exactly one rule, run honestly — a comparison, a distance, a cell counting its neighbours, a gradient — and the two that would keep running past the last one prove they are still running whether or not it looks like anything is happening.
EXHIBIT I · SORTING ALGORITHMS
O(n²) and O(n log n) are not two speeds of the same thing. Past a few hundred elements one of them stops being a claim about big numbers and becomes something you can watch — or, with sound on, hear: the quadratic lanes' comparison rate visibly collapses as n grows, while merge, quick and heap barely slow down.
All six race the same shuffled array, one comparison at a time, so the picture is a fair fight rather than six separate demos. Pick a lane to listen to — pitch tracks the value, not the position, which is what "nearly sorted" sounds like as it closes in from both ends.
n and speed change the race · listen to a lane for sound
EXHIBIT II · GRAPH SEARCH
Dijkstra explores strictly by distance travelled so far. A* explores by that distance plus a guess about what is left — and the guess is the entire speed-up. Turn it off (w=0) and A* degrades exactly to Dijkstra; turn it up too far and the guess can be wrong, and the path stops being the shortest one.
All three algorithms flood the same maze, drawn side by side, shaded by the order each cell was visited. Watch the panels for A* burn far fewer cells than Dijkstra's while finding an equally short path — until the weight slider is pushed past honest and it finds a shorter-looking path that is not actually shortest.
drag to draw walls · generate maze · weight bends A* toward greedy
EXHIBIT III · CELLULAR AUTOMATA
A cell that looks at eight neighbours and a cell that looks at two are the same kind of object. On the left, Conway's Life — draw cells, or drop a glider, a spaceship, a glider gun. On the right, elementary Rule 110 — a single row of cells, each one a function of itself and its two neighbours, drawn one generation at a time as it falls down the canvas.
Rule 110 was proved Turing-complete in 2004. Life almost certainly is too, once you allow arbitrarily large patterns — a computer built entirely from gliders has been built inside it. Both of these can, in principle, run this website.
draw on the Life grid · pick a pattern · Rule 110 runs on its own
EXHIBIT IV · MACHINE LEARNING
Nothing here is told what a spiral is. A small network is given points and one bit each — which side — and gradient descent is the whole explanation for why a wiggling boundary eventually separates them, when it can. It runs in a Worker, so it keeps learning while you scroll away.
Watch it fail on the spiral with too few hidden units, on purpose — a network that always succeeds would teach nothing about why width and depth matter. Widen it, and the same gradient, given more room to bend, finds the arms.
it trains in a worker · widen it if the spiral defeats it
EXHIBIT V · INFORMATION THEORY
A symbol that shows up often is expensive to spell out in full every single time. Huffman's algorithm is the proof, by construction, that short codes for common symbols and long codes for rare ones is not merely sensible — it is optimal among every prefix code there is. Shannon's entropy is the number that says exactly how much better no code could ever do.
Type anything. The tree assembles itself bottom-up, two lowest-frequency nodes at a time, and the code table fills in as each leaf is reached. The gap between the entropy and what this specific tree achieves is usually a few percent — Huffman's whole argument, stated as a measured number instead of a theorem.
type in the box · watch the tree build · presets try the edge cases