Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Gives lattice points in a variety of arrangements
ResourceFunction["LatticePointsArrangement"][arrangement,n] generates the first n lattice points based on arrangement. |
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ResourceFunction["LatticePointsArrangement"][] returns all the possible arrangements. |
"CCWSpiralEast" |
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"CCWSpiralNorth" |
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"CCWSpiralWest" |
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"CCWSpiralSouth" |
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"CWSpiralEast" |
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"CWSpiralNorth" |
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"CWSpiralWest" |
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"CWSpiralSouth" |
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"CCWDiamondEast" |
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"CCWDiamondNorth" |
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"CCWDiamondWest" |
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"CCWDiamondSouth" |
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"CWDiamondEast" |
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"CWDiamondNorth" |
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"CWDiamondWest" |
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"CWDiamondSouth" |
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"ZigZagEastQ1" |
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"ZigZagNorthQ1" |
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"ZigZagWestQ2" |
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"ZigZagNorthQ2" |
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"ZigZagWestQ3" |
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"ZigZagSouthQ3" |
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"ZigZagEastQ4" |
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"ZigZagSouthQ4" |
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"ZigZagEastQ12" |
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"ZigZagWestQ12" |
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"ZigZagNorthQ23" |
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"ZigZagSouthQ23" |
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"ZigZagWestQ34" |
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"ZigZagEastQ34" |
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"ZigZagNorthQ14" |
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"ZigZagSouthQ14" |
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"ZigZagNorthEastQ12" |
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"ZigZagNorthWestQ12" |
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"ZigZagWestNorthQ23" |
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"ZigZagWestSouthQ23" |
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"ZigZagSouthEastQ34" |
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"ZigZagSouthWestQ34" |
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"ZigZagWestSouthQ14" |
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"ZigZagWestNorthQ14" |
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"ZigZagEastQ123" |
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"ZigZagSouthQ123" |
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"ZigZagNorthQ234" |
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"ZigZagEastQ234" |
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"ZigZagEastQ134" |
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"ZigZagNorthQ134" |
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"ZigZagEastQ124" |
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"ZigZagSouthQ124" |
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"ZigZagNorthWestQ123" |
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"ZigZagWestNorthQ123" |
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"ZigZagWestSouthQ234" |
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"ZigZagSouthWestQ234" |
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"ZigZagSouthEastQ134" |
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"ZigZagEastSouthQ134" |
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"ZigZagNorthEastQ124" |
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"ZigZagEastNorthQ124" |
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"ZigZagNorthEastQ123" |
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"ZigZagWestSouthQ123" |
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"ZigZagWestNorthQ234" |
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"ZigZagSouthEastQ234" |
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"ZigZagSouthWestQ134" |
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"ZigZagEastNorthQ134" |
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"ZigZagNorthWestQ124" |
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"ZigZagEastSouthQ124" |
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"DiagonalZigZagEastQ1" |
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"DiagonalZigZagNorthQ1" |
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"DiagonalZigZagNorthQ2" |
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"DiagonalZigZagWestQ2" |
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"DiagonalZigZagSouthQ3" |
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"DiagonalZigZagWestQ3" |
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"DiagonalZigZagEastQ4" |
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"DiagonalZigZagSouthQ4" |
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"DiagonalZigZagEastQ12" |
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"DiagonalZigZagSouthQ23" |
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"DiagonalZigZagNorthQ23" |
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"DiagonalZigZagEastQ34" |
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"DiagonalZigZagWestQ34" |
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"DiagonalZigZagNorthQ14" |
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"DiagonalZigZagWestQ12" |
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"DiagonalZigZagSouthQ14" |
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"DiagonalZigZagEastQ123" |
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"DiagonalZigZagSouthQ123" |
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"DiagonalZigZagNorthQ234" |
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"DiagonalZigZagEastQ234" |
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"DiagonalZigZagWestQ134" |
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"DiagonalZigZagNorthQ134" |
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"DiagonalZigZagWestQ124" |
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"DiagonalZigZagSouthQ124" |
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"CCWDiagonalQ1" |
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"CWDiagonalQ1" |
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"CCWDiagonalQ2" |
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"CWDiagonalQ2" |
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"CCWDiagonalQ3" |
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"CWDiagonalQ3" |
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"CWDiagonalQ4" |
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"CCWDiagonalQ4" |
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"CCWDiagonalQ12" |
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"CWDiagonalQ23" |
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"CCWDiagonalQ23" |
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"CWDiagonalQ34" |
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"CCWDiagonalQ34" |
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"CWDiagonalQ14" |
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"CWDiagonalQ12" |
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"CCWDiagonalQ14" |
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"CCWDiagonalQ123" |
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"CWDiagonalQ123" |
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"CCWDiagonalQ234" |
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"CWDiagonalQ234" |
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"CCWDiagonalQ134" |
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"CWDiagonalQ134" |
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"CCWDiagonalQ124" |
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"CWDiagonalQ124" |
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"CWCornerQ1" |
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"CCWCornerQ3" |
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"CWCornerQ2" |
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"CCWCornerQ4" |
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"CWCornerQ3" |
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"CCWCornerQ1" |
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"CWCornerQ4" |
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"CCWCornerQ2" |
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"CWCornerQ12" |
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"CCWCornerQ12" |
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"CCWCornerQ23" |
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"CWCornerQ23" |
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"CCWCornerQ34" |
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"CWCornerQ34" |
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"CCWCornerQ14" |
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"CWCornerQ14" |
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"CWCornerQ123" |
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"CCWCornerQ123" |
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"CWCornerQ234" |
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"CCWCornerQ234" |
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"CWCornerQ134" |
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"CCWCornerQ134" |
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"CWCornerQ124" |
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"CCWCornerQ124" |
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Create 20 points in a counterclockwise spiral starting in the eastern direction:
In[1]:= |
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Out[1]= |
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Create some points based on zigzagging diagonally in the first two quadrants:
In[2]:= |
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Visualize the points:
In[3]:= |
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Out[3]= |
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LatticePointsArrangement without any arguments returns all the possible arrangements:
In[4]:= |
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Out[4]= |
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Currently 136 arrangements are known:
In[5]:= |
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Out[5]= |
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Create the Ulam prime spiral:
In[6]:= |
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Out[7]= |
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Recreate the OEIS A316667 sequence of a horse moving on a spirally numbered board and moving to the lowest available unvisited square at each step:
In[8]:= |
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Out[15]= |
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This work is licensed under a Creative Commons Attribution 4.0 International License