Dot-to-Dot Puzzle Maker
Printable dot-to-dot puzzles built from curves, not hand-placed points. Dots are spaced evenly along the line, and crowding is measured not guessed.
How the dots are placed
- Every shape here is a curve rather than a list of points somebody typed. A star is ten straight edges worked out from an angle, a heart is the standard parametric one, a flower is a rose curve — so there are no coordinates to have mistyped, and adding a shape means adding a formula.
- The dots are placed at equal distance ALONG the curve, not at equal steps of the parameter. Stepping the parameter is easier and, on a curved shape, visibly wrong: on the heart it puts the widest gap at ten times the narrowest, and on the spiral at seven times. The star and the octagon are the exceptions — their edges are all the same length, so the parameter already runs at a steady speed and stepping it comes out perfectly even. They are the reason this has to be measured per shape rather than assumed.
- Bunched dots are not a cosmetic problem. If dot 14 is nearer to dot 30 than to dot 15, the puzzle is ambiguous and a child draws the wrong line, so the tool measures how close any two non-neighbouring dots come and warns when that gap drops below the spacing between neighbours.
- That measurement also gives each shape a natural limit. A crescent has two horns that nearly touch, so it takes fewer dots than an octagon before it stops reading clearly — and the tool works that number out rather than guessing it.
- The spiral is the only shape here that does not join back to itself, which is why its last dot is genuinely the end rather than a return to the first.
How to use
- Pick a picture and how many dots you want.
- Turn the answer lines on if you want to check it.
- Print it.
Frequently asked questions
Where do the shapes come from?
Each one is a curve rather than a list of coordinates somebody typed — a star is ten edges worked out from an angle, a heart is the standard parametric one, a flower is a rose curve. There is nothing transcribed, so there is nothing to have transcribed wrongly, and adding a shape means adding a formula.
Why does the dot count have a minimum as well as a maximum?
Because crowding runs both ways, which was a surprise. A crescent’s horns bring two parts of the outline together, so too many dots make it ambiguous. But a spiral’s arms sit a fixed distance apart, so too FEW dots leave a bigger gap along the curve than between the arms — and it only becomes clear once you add more.
What makes a dot-to-dot ambiguous?
A dot having a stranger nearer to it than its own successor. If dot 14 is closer to dot 30 than to dot 15, a child draws the wrong line and the picture is ruined. The tool measures that distance on every pair and refuses to pretend a crowded puzzle is fine.
Are the dots really evenly spaced?
Along the curve, yes, and it is checked by an exact identity rather than by eye: asking for twice as many dots and taking every other one gives back precisely the original answer. Straight-line gaps vary a little on angular shapes, because a pair of dots either side of a star’s point is closer as the crow flies.
Why not just step the parameter evenly?
Because it is visibly wrong. On a heart, stepping the parameter puts the dots more than forty per cent out of even, bunching them where the curve moves slowly and stretching them where it races. Walking the accumulated distance instead is the harder thing to do and the only one that looks right.
Can I check the answer?
Yes — turn on the answer lines and the finished drawing appears joined up. It prints without the controls, so the sheet that comes out is just the puzzle.
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