Quilt Block Layout Explorer
One asymmetric block tiled four-up makes exactly 70 distinct quilts under rotation — counted two independent ways.
Click any block to turn it a quarter. Nothing about the block changes — only which way it faces.
One block, seventy quilts
What makes quilting a design activity rather than a construction one is that the block is not the quilt. Take one asymmetric block, tile it four up, and let each copy sit at any of its four rotations. That is 4⁴ = 256 arrangements — but many are the same quilt seen from a different side of the table.
Counting the genuinely distinct ones is Burnside's lemma over the rotations of the tile: (256 + 4 + 16 + 4) ÷ 4 = 70. A brute-force enumeration that canonicalises every arrangement agrees exactly — two independent methods, same answer, which is the only reason to believe a counting argument at all. Allow reflections and it collapses to 39.
Seventy different quilts from one block and a rotation. Barn Raising, Straight Furrows, Streak of Lightning and Sunshine and Shadow are all the same log cabin block — the design is entirely in the turning. And the space explodes with the tile: a 3×3 has 262,144 raw arrangements before you even start removing duplicates.
The small case you can check by hand
If seventy feels like a lot to take on trust, try the smaller one. A four-patch coloured in two values has 2⁴ = 16 colourings, and under rotation those collapse to exactly 6: all light, all dark, one light corner, one dark corner, two adjacent, two diagonal. Six looks, and you can lay them out on a table in a minute. Burnside gives (16 + 2 + 4 + 2) ÷ 4 = 6 too.
Notes
- A symmetric block cannot do this. A nine-patch looks the same at every rotation, so turning it changes nothing — which is why the blocks with famous layout variations are all asymmetric. Pick the nine-patch above and the shuffle button stops having any effect, which is the point.
- Value placement is what you are actually designing. The secondary patterns come from where the lights and darks land across block boundaries, not from inside any single block. That is why the same layout in different fabrics can look like a different quilt.
- Photograph it in greyscale before committing. The value sorter explains why — what reads as contrast on screen is often much flatter in cloth.
- Try the shuffle a few times. Most random arrangements look like noise, which is itself informative: the named layouts are named because they are the few that resolve into something.
How to use
- Pick a block and a grid size, then click blocks to turn them.
- Try the named log cabin settings — they are all the same block.
- Change the light and dark colours to see what value placement does.
- Shuffle a few times to see how few arrangements actually resolve.
Frequently asked questions
How many quilts can you make from one block?
From a single asymmetric block tiled four-up with free rotation, exactly 70 distinct designs. There are 256 raw arrangements, but many are the same quilt seen from another side of the table — Burnside's lemma gives (256 + 4 + 16 + 4) ÷ 4 = 70, and a brute-force enumeration agrees exactly.
Why do Barn Raising and Straight Furrows look so different?
They are the same log cabin block. The entire difference is which way each copy faces. That is the point this tool exists to make visible — the block is not the quilt, and the design lives in the turning.
Does allowing mirror images change the count?
Yes, it collapses to 39. Whether that is the right count depends on your quilt: a mirrored layout is genuinely different if the fabric has a direction, and identical if it does not.
Why does rotating a nine-patch do nothing?
Because it is symmetric under rotation — it looks the same at every quarter turn, so there is nothing to arrange. That is exactly why the blocks with famous layout variations are all asymmetric ones, and it is worth trying in the tool to see the contrast.
What is a secondary pattern?
A shape that appears across block boundaries rather than inside any single block — pinwheels, chains and stars that no individual block contains. They come from where the lights and darks land when blocks meet, which is why value placement matters more than the block design.
Is there a simpler case I can check by hand?
Yes. A four-patch coloured in two values has 16 colourings, which collapse under rotation to exactly six: all light, all dark, one light corner, one dark corner, two adjacent, two diagonal. You can lay them on a table in a minute, and Burnside gives six too.
How many layouts does a bigger grid have?
Astronomically more — a 3 by 3 tile of rotatable blocks has 262,144 raw arrangements before removing duplicates. The exact count stops being the interesting number; what matters is that one block is a whole design space rather than a single quilt.
Does this send anything anywhere?
No. Everything runs in your browser and nothing is stored or uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.