Gfis: Created page with "===Hexagonal grid, counterclockwise=== Cf. [https://oeis.org/A056105 A056105] First spoke of a hexagonal spiral. From Robert G. Wilson v, Jul 05 2014: (Start) Each of the 6 primary spokes or rays has a generating formula as stated here: 1st: 90 degrees A056105 3n^2 - 2n + 1 2nd: 30 degrees A056106 3n^2 - n + 1 3rd: 330 degrees A056107 3n^2 + 1 4th: 270 degrees A056108 3n^2 + n + 1 5th: 210 degrees A056109 3n^2 + 2n + 1 6th: 150 degrees A003215 3n^2 + 3n..."

2024-12-04T10:00:42Z

Created page with "===Hexagonal grid, counterclockwise=== Cf. [https://oeis.org/A056105 A056105] First spoke of a hexagonal spiral. From Robert G. Wilson v, Jul 05 2014: (Start) Each of the 6 primary spokes or rays has a generating formula as stated here: 1st: 90 degrees A056105 3n^2 - 2n + 1 2nd: 30 degrees A056106 3n^2 - n + 1 3rd: 330 degrees A056107 3n^2 + 1 4th: 270 degrees A056108 3n^2 + n + 1 5th: 210 degrees A056109 3n^2 + 2n + 1 6th: 150 degrees A003215 3n^2 + 3n..."

New page

===Hexagonal grid, counterclockwise===
Cf. [https://oeis.org/A056105 A056105] First spoke of a hexagonal spiral.
From Robert G. Wilson v, Jul 05 2014: (Start)
Each of the 6 primary spokes or rays has a generating formula as stated here:
1st: 90 degrees A056105 3n^2 - 2n + 1
2nd: 30 degrees A056106 3n^2 - n + 1
3rd: 330 degrees A056107 3n^2 + 1
4th: 270 degrees A056108 3n^2 + n + 1
5th: 210 degrees A056109 3n^2 + 2n + 1
6th: 150 degrees A003215 3n^2 + 3n + 1
Each of the 6 secondary spokes or rays has a generating formula as stated here:
1st: 60 degrees 12n^2 - 27n + 16
2nd: 360 degrees 12n^2 - 25n + 14
3rd: 300 degrees 12n^2 - 23n + 12
4th: 240 degrees 12n^2 - 21n + 10
5th: 180 degrees 12n^2 - 19n + 8
6th: 120 degrees 12n^2 - 17n + 6 = A033577(n+1)
===Square grid, counterclockwise===
Cf. [https://oeis.org/A244677 A244677] The spiral of Champernowne, read along the East ray.
Robert G. Wilson v, [https://oeis.org/A244677/a244677.jpg Cover of the March 1964 issue of Scientific American]
Formulas for rays in directions of 32 compass points:
SE 4n^2 -4n +1
SExS 64n^2 -113n +50
SSE 16n^2 -25n +10
SxE 64n^2 -115n +52
S 4n^2 -5n +2
SxW 64n^2 -117n +54
SSW 16n^2 -27n +12
SWxS 64n^2 -119n +56
SW 4n^2 -6n +3
SWxW 64n^2 -121n +58
WSW 16n^2 -29n +14
WxS 64n^2 -123n +60
W 4n^2 -7n +4
WxN 64n^2 -125n +62
WNW 16n^2 -31n +16
NWxW 64n^2 -127n +64
NW 4n^2 -8n +5
NWxN 64n^2 -129n +66
NNW 16n^2 -33n +18
NxW 64n^2 -131n +68
N 4n^2 -9n +6
NxE 64n^2 -133n +70
NNE 16n^2 -35n +20
NExN 64n^2 -135n +72
NE 4n^2 -10n +7
NExE 64n^2 -137n +74
ENE 16n^2 -37n +22
ExN 64n^2 -139n +76
E 4n^2 -11n +8
ExS 64n^2 -141n +78
ESE 16n^2 -39n +24
SExE 64n^2 -143n +80

OEIS/Spirals - Revision history