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'''[[Main Page|Home]] * [[Programming]] * [[Algorithms]] * Traversing Subsets of a Set'''
[[File:Hypercubeorder_binary.svg|thumb|right|link=https://commons.wikimedia.org/wiki/File:Hypercubeorder_binary.svg|4D-hypercube <ref>The [https://en.wikipedia.org/wiki/Four-dimensional_space|4D]]-[https://en.wikipedia.org/wiki/Hypercube hypercube], layered according to distance from one corner. As described in "[[Alice|Alice in Wonderland]]" by the [https://en.wikipedia.org/wiki/Cheshire_Cat Cheshire Cat], this vertex-first-shadow of the [https://en.wikipedia.org/wiki/Tesseract tesseract] forms a [https://en.wikipedia.org/wiki/Rhombic_dodecahedron rhombic dodecahedron]. Note that the two central (green) vertices should coincide if using an orthogonal projection from 4 to 3 dimensions, but were drawn here slightly apart. The eight [[Nibble|nibbles]] with odd binary digit sums form a cube and are marked in white. The two [https://en.wikipedia.org/wiki/Palindrome palindromes] 0110 and 1001 (compare XOR and XNOR) are projected in the center of the rhombic dodecahedron and are marked in green. The other six nibbles with even binary digit sums form an [https://en.wikipedia.org/wiki/Octahedron octahedron] and are marked in blue, image by Lipedia, 2010, [https://en.wikipedia.org/wiki/Hasse_diagram Hasse diagram from Wikipedia]</ref>]]
'''Traversing Subsets of a Set''' determines the [https://en.wikipedia.org/wiki/Power_set power set] of a set, or a subset of the power set with certain properties such as equal [https://en.wikipedia.org/wiki/Cardinality cardinality]. Represented by a [[Bitboards|bitboard]], this is useful to loop over possible [[Occupancy|occupancies]] of a set of rays or lines, and to [[Looking for Magics|look for]] [[Magic Bitboards|magic factors]] with a certain cardinality.
