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Patrick2788
Silver Contributor
Jul 18, 2023

Formula Challenge: The most efficient way to generate a Number Spiral (Ulam spiral) ?

The goal: Ulam spiral - Wikipedia   The trick is creating a function capable of producing the largest matrix of numbers possible (this may rule out the recursive approach).   The approach ...
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Formulas and Functions
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Patrick2788's avatar
Patrick2788
Silver Contributor
Nov 21, 2024

This is my rendition for 2024 with  no Lambda helper functions.

//Patrick2788   11/21/2024

//Create a Ulam Spiral by supplying cartesian coordinates.
//Parameters:
//rings -   Create a spiral with this many rings from the center starting value
//[start_at] -  Specify a starting number. Defaults to 1 if omitted.

SpiralĪ» = LAMBDA(rings,[start_at],
        LET(
            start_at,IF(ISOMITTED(start_at),1,start_at),
        //Create cartesian coordindates
            i, SEQUENCE(rings * 2 + 1, , rings, -1),
            j, SEQUENCE(, rings * 2 + 1, -rings, 1),
        //Broadcast cartesian coordinates to matrices
            x, j * SEQUENCE(rings * 2 + 1, , 1, 0),
            y, i * SEQUENCE(, rings * 2 + 1, 1, 0),
        //Four scenarios for Four quadrants:
        //a_ - right    b_ -    left    c_ - top    d_ - bottom
            a_, (ABS(x) > ABS(y)) * (x > 0),
            b_, (ABS(x) > ABS(y)) * (x <= 0),
            c_, (ABS(x) <= ABS(y)) * (y > 0),
            d_, (ABS(x) <= ABS(y)) * (y <= 0),
        //Calculations for each quadrant:
            a, 4 * x ^ 2 - 3 * x + y,
            b, 4 * x ^ 2 - x - y,
            c, 4 * y ^ 2 - y - x,
            d, 4 * y ^ 2 - 3 * y + x,
        //Check cartesian coordinates, apply calculations
            result, start_at+IF(a_, a, IF(b_, b, IF(c_,c, d))),
            result
        )
    );

 

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