       Re: simplifying ulam spiral code

• To: mathgroup at smc.vnet.net
• Subject: [mg56423] Re: [mg56394] simplifying ulam spiral code
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 24 Apr 2005 03:29:30 -0400 (EDT)
• References: <200504230516.BAA03185@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```This is somewhat "functional" and agrees (I think) with the picture at the link (depending on where we start, which isn't actually revealed).

Clear[side, ell]
next = {{0, -1}, {1, 0}};
initial = {start = {0, 0}, {1, 0}, 1};
side[i_]@{corner_, direction_, count_} :=
{Nest[Sow[# + direction] &, corner, count],
next.direction, count + i}
ell@{corner_, direction_, count_} :=
side@side@{corner, direction, count}
limit = Ceiling[(1 + Sqrt[1 + 4*20000])/2];
list = Pick[#, PrimeQ@Range@Length@#] &
@Prepend[First@Last@Reap@Nest[ell, initial, limit], start];
ListPlot[list, PlotStyle -> PointSize[0.007],
AspectRatio -> Automatic, Axes -> True];

The posted code gives {1,1} and {0,1} as the first two colored squares, which means the direction followed on the second side is {-1,0}, since {1,1}+{-1,0}=={0,1}. The picture at the link would have {0,1} as the direction taken on the second side.

Possibly the posted code winds clockwise or plots x and y reversed, or something.

Bobby

On Sat, 23 Apr 2005 01:16:49 -0400 (EDT), zak <chocolatez at gmail.com> 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
>
>
>
>

--
DrBob at bigfoot.com

```

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