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Re: simplifying ulam spiral code

• To: mathgroup at smc.vnet.net
• Subject: [mg56407] Re: simplifying ulam spiral code
• From: Peter Pein <petsie at arcor.de>
• Date: Sun, 24 Apr 2005 03:28:57 -0400 (EDT)
• References: <d4cmlr$39e$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

zak wrote:
> hi
> in the site:
> http://teachers.crescentschool.org/weissworld/m3/spiral/spiral.html
> there is a mathematica code for drawing ULAM'S SPIRAL
> the code is:
> 
> dat = Table[i, {i, 20000}];
> x := 0; y := 0; num := 1; shift := 1;
> point := {x, y}; list = {}
>  While[num <= 20000,
>   i := 1;
>   While[i <= shift,
>     x = x + 1;
>     If[PrimeQ[dat[[num]]] == True, list = Flatten[{list, point}]]; num++; 
>     i++;]; i := 1; While[i <= shift,
>     y = y + 1;
>     If[PrimeQ[dat[[num]]] == True, list = Flatten[{list, point}]]; num++; 
>     i++;]; shift++;
>   i := 1;
>   While[i <= shift,
>     x = x - 1;
>     If[PrimeQ[dat[[num]]] == True, list = Flatten[{list, point}]]; num++; 
>     i++;]; i := 1;
>   While[i <= shift,
>     y = y - 1;
>     If[PrimeQ[dat[[num]]] == True, list = Flatten[{list, point}]]; num++; 
>     i++;]; shift++;]
>  ListPlot[Partition[list, 2], PlotStyle -> PointSize[0.007], 
>     AspectRatio -> Automatic, Axes -> True];
> 
> 
> or see text in:
> http://sr1.mytempdir.com/15902
> 
> 
> Please i hope someone transform it to a functional programming code.
> thanks
> zak
> 
Hi Zak,

This is my approach:

 First, create a complete spiral and then delete the points which
correspond to non-primes.

spiral[n_Integer /; n > 0] := Module[{
  lst = Take[FoldList[Plus, {0, 0}, Join @@
    Table[Join @@ Transpose[
      Table[(-1)^(k + 1)*{{1, 0}, {0, 1}}, {k}]],
      {k, Ceiling[(Sqrt[1 + 4n] - 1)/2]}]],
     n]},
  ListPlot[Delete[lst, List /@
    Complement[Range[n], Prime[Range[PrimePi[n]]]]],
    Axes -> False, PlotStyle -> PointSize[.007],
    AspectRatio -> Automatic]
]

spriralplot[20000] will (hopefully ;-)) give the same image, as the
above so called Mathematica code.

-- 
Peter Pein
Berlin