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Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f . g) z. The implementation of map above on singly linked lists is not tail-recursive, so it may build up a lot of frames on the stack when called with a large list. Many languages ...
The map folding and stamp folding problems are related to a problem in the mathematics of origami of whether a square with a crease pattern can be folded to a flat figure. If a folding direction (either a mountain fold or a valley fold ) is assigned to each crease of a strip of stamps, it is possible to test whether the result can be folded ...
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites. The napkin folding problem is the problem of whether a square or rectangle of paper can be folded so the perimeter of the flat figure is greater than that of the original square.
Although Kawasaki's theorem completely describes the folding patterns that have flat-folded states, it does not describe the folding process needed to reach that state. For some (multi-vertex) folding patterns, it is necessary to curve or bend the paper while transforming it from a flat sheet to its flat-folded state, rather than keeping the ...
It includes the NP-completeness of testing flat foldability, [2] the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat), [2] [4] the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns, [2] [4] the fold-and ...
The Miura fold (ミウラ折り, Miura-ori) is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Kōryō Miura. [1] The crease patterns of the Miura fold form a tessellation of the surface by parallelograms.
A common source of such sensitivity to initial conditions is that the map represents a repeated folding and stretching of the space on which it is defined. In the case of the logistic map, the quadratic difference equation describing it may be thought of as a stretching-and-folding operation on the interval (0,1) .