A paperfolding paradise
The website of writer and paperfolding designer David Mitchell
|Minimalist, Single Sheet, Square, Pattern Forming Puzzles - Summary Page|
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.