• To: mathgroup at smc.vnet.net
• Subject: [mg56905] Hexagonal Spiral AddOn
• From: zak <chocolatez at gmail.com>
• Date: Tue, 10 May 2005 03:42:08 -0400 (EDT)
• Reply-to: zak <chocolatez at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi
as an addon to my previous message, i have found in an article titled
a method to draw a spiral on a hexagonal grid written in UBASIC
programming language , i have translated some of the ubasic lines to
mathematica,
http://sr2.mytempdir.com/25816
indeed i could not visualize the code, but as you can see the prime
numbers in the graph will have some ordering , i color the 7, 19,  37,
61 sequence wich appeared in the
http://www.cut-the-knot.org/ctk/HexMosaic.gif
you will see them in a line, so the code are working.
here is the contents of the above notebook: the socond graph will show
you how the points are arranged in hexagonal grid, but what annoy me
is the crooked line wich connect the points because it will not
connect at the center of every hexagon.

dx = {2, 1, -1, -2, -1, 1};
dy = {0, 2, 2, 0, -2, -2};
x = 0; y = 0 ;
lst = {}; z = 0; v = {};
For[shell = 1, shell < 200,
x = x + dx[[5]]; y = y + dy[[5]];
For[k = 1, k <= 6,
For[n = 1, n <= shell,
x = x + dx[[k]]; y = y + dy[[k]]; z = z + 1;
If [PrimeQ[z] == True,
lst = Join[lst, {{x, y}, {x + 1, y + 1}}]];

If[MatchQ[z, 7 | 19 | 37 | 61], v = Join[v, {{x, y}}]];

, n++]; k++]; shell++];
p1 = Graphics[{PointSize[0.001], Point /@ lst}];
p2 = Graphics[{Red, PointSize[0.005], Point[{2, 0}], Point /@ v}];
Show[p1, p2, AspectRatio -> Automatic]

dx = {2, 1, -1, -2, -1, 1};
dy = {0, 2, 2, 0, -2, -2};
x = 0; y = 0 ;
lst = {};

For[shell = 1, shell < 8,
x = x + dx[[5]]; y = y + dy[[5]];
For[k = 1, k <= 6,
For[n = 1, n <= shell,
x = x + dx[[k]]; y = y + dy[[k]];

lst = Join[lst, {{x, y}, {x + 1, y + 1}}];

, n++]; k++]; shell++];
p1 = Graphics[{Line[Take[lst, 38]], Point /@ lst}];
p2 = Graphics[{Red, PointSize[0.015], Point[{0, 0}]}];
Show[p1, p2, AspectRatio -> Automatic]

```

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