Complete The Pattern Generator

A row of tiles runs left to right, and something about them changes as it goes: which shape it is, how far it is turned, how the line is drawn, or how many of it there are. One tile is missing. The reader works out the rule and picks the tile that belongs in the gap. What makes this worth setting rather than filling with more shapes is that the difficulty is the rule: an easy row has one thing repeating on a short cycle, and the hardest has three things changing at once, one of which climbs and then comes back down.

Difficulty

Seed (optional)

The same seed rebuilds the same pattern. Deterministic, not cryptographic.

A row of shapes with one missing, and a few tiles to choose between, will appear here.

What this generator does

Chooses one to three rules, builds the whole row from them, hides a tile, and offers a set of choices of which exactly one fits.

How to use this tool

Choose a difficulty. It changes how the rule works, not how long the row is.
Read the row from left to right and work out what is changing.
Look at the gap and decide what the rule demands there.
Pick the matching tile from the choices below the row.
Show the answer to check, and to read the rule stated plainly.

Understanding the controls

Difficulty: One thing changing on a short cycle at the easiest, three at once at the hardest — including one that climbs and then comes back down, which cannot be read from two tiles alone.
Seed (optional): Type anything to rebuild the same row later, which is how you reprint a sheet you have lost. Seeds here are for repeating a puzzle: deterministic, not cryptographic.

Common use cases

An early-years or key-stage-one pattern exercise, made fresh each time
A reasoning warm-up that is not arithmetic
A puzzle for a reader who has outgrown the two-shape ABAB row
A quick assessment of whether a rule is being read or a guess is being made
Reprinting the identical row later from its seed

How this generator works

Each tile is four things a reader can see: a shape, a turn, a way of drawing the line and a number of copies. A rule says how one of those moves along the row — walking a list and wrapping round, adding a fixed amount, or climbing to a limit and coming back down. The whole row is then a function of position, so the answer is not a matter of taste: it is what the rule gives at the gap. Before a row is published it is rebuilt from its own rules and compared tile by tile, and every choice offered is tested, so that exactly one of them fits. Two things are refused outright, both because they would make the difficulty a fiction rather than a fact: a rule that does not visibly change anything across the row, and a turn applied to a shape that is nearly its own rotation, which is measured rather than assumed — a rosette turned a quarter barely moves, so it is never turned.

Randomness and fairness

The rules, the shapes and which tile is hidden come from your browser's cryptographic random source. Type a seed to get the same row back another day: a seed is deterministic, not cryptographic, and gives away nothing worth protecting.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

The gap is never the first or second tile, because a rule cannot be read from nothing.
A row carries at most three rules; beyond that it reads as a list rather than a pattern.
Only four things about a tile can change, so a rule is always about one of those four.
A harder level is a more complicated rule, not a longer row — which some readers will find easier, not harder.

Privacy and your data

The pattern, the choices and the answer are all worked out in your browser. Nothing you type as a seed, and no puzzle made from it, leaves the device.