Origami Heaven

The website of writer and paperfolding designer David Mitchell

Minimalist, Single Sheet, Square, Pattern Forming Puzzles - Summary Page

In pattern making puzzles of this kind the object is to fold a specified square pattern on either just one, or both surfaces of the paper (irrespective of orientation), or to produce that pattern on one surface of the paper and its reverse / negative on the other, in each case using as few active folds as possible. I call these the single sided, double sided and negative modes.

Puzzles of this kind are easy to set. Simple think of a pattern ... However, not all such puzzles are created equal.

The table below shows a selection of square patterns, some very easy to solve, and some quite difficult, which I have given names in order to make it easier to refer to them. The information below the names gives what I think is the minimum number of folds required to solve the pattern in each of the three possible modes. You will see that sometimes solving the negative mode requires less folds than solving the double sided mode. Where no figure is given it means that I have not explored this particular pattern or mode fully enough to be confident I know what the minimum figure is. You may enjoy finding out for yourself.

All these patterns and modes function as puzzles ... but some function better than others. Where I think that one of the modes offers a challenge particularly worth taking on, and this site contains diagrams for what I think is the minimal solution,. the name of the pattern links to a more formal presentation of the puzzle and the mode links to the solution.

Please let me know if you can solve any of these patterns using fewer active folds than I have indicated.

It is also worth noting that puzzles of this kind often have multiple solutions ... some of which may be interesting to fold even if they are not minimal. Sometimes there are several different minimal solutions.

 Half and HalfSingle Sided - 2 Double Sided - Negative (not possible) CornerSingle Sided - 2 Double Sided - 5 Negative - 3 ChequerboardSingle Sided - 4 Double Sided - 4 Negative (not possible) Yin YangSingle Sided - Double Sided - Negative (not possible) HarlequinSingle Sided - 4 Double Sided - 4 Negative (not possible) FlashSingle Sided - 5 Double Sided - Negative - Double FlashSingle Sided - Double Sided - Negative - Triple FlashSingle Sided - Double Sided - Negative - Single RotorSingle Sided - Double Sided - Negative - Double RotorSingle Sided - 12 Double Sided - Negative - ZigzagSingle Sided - 8 Double Sided - Negative (not possible) WindowSingle Sided - 5 Double Sided - Negative - TwisterSingle Sided - 4 Double Sided - Negative - StripeSingle Sided - Double Sided - Negative - 6 Four SquaresSingle Sided - 5 Double Sided - Negative - KSingle Sided - Double Sided - 5 Negative - ChevronsSingle Sided - 5 Double Sided - Negative - Double KSingle Sided - Double Sided - 15 Negative (not possible) JanusSingle Sided - Double Sided - 6 Negative (not possible) ModusSingle Sided - 10 Double Sided - Negative (not possible) PhoenixSingle Sided - 11 Double Sided - Negative (not possible) SisyphusSingle Sided - Double Sided - Negative - Three RaysSingle Sided - 4 Double Sided - Negative - Four RaysSingle Sided - 6 Double Sided - Negative - Five RaysSingle Sided - 8 Double Sided - Negative -