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Map folding is the question of how many ways there are to fold a rectangular map along its creases, allowing each crease to form either a mountain or a valley fold. It differs from stamp folding in that it includes both vertical and horizontal creases, rather than only creases in a single direction.
Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as map fusion and is the functional analog of loop fusion. [2] 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 .
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) .
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.
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 ...
In the simplest form, it is 1 for all neurons close enough to BMU and 0 for others, but the Gaussian and Mexican-hat [9] functions are common choices, too. Regardless of the functional form, the neighborhood function shrinks with time. [6] At the beginning when the neighborhood is broad, the self-organizing takes place on the global scale.
The Miura fold is related to the Kresling fold, the Yoshimura fold and the Hexagonal fold, and can be framed as a generalization of these folds. [ 3 ] The Miura fold is a form of rigid origami , meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat.