Guilloche Pattern

Author

Eric W. Weisstein
June 28, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Graphics/GuillochePattern.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GuillochePattern.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Original Code By

Ed Pegg Jr.
Wolfram Research, Inc.
September 11, 2002

Graphic

V5

Show[GraphicsArray[#[Evaluate[Flatten[{
Table[(1.2 +.4 Sin[3 x +.5]) +((4 + Sin[5 x]) - (1.2+.4 Sin[3 x +.5])) (1+Sin[3 x + (n +  .2 Sin[100 x])/ Pi])/2,{n,0,19}],
Table[(4 + Sin[5 x]) +((7 + Sin[7 x]) - (4+ Sin[5 x])) (1+Sin[5 x + n/ Pi])/2,{n,0,19}],
Table[(7 + Sin[7 x]) +((10 + Sin[4 x +4.7]) - (7+ Sin[7 x])) (1+Sin[4 x + n/ Pi])/2,{n,0,19}],
Table[(7 + Sin[7 x]) +((10+ Sin[4 x + 4.7]) - (7+ Sin[7 x])) (1+Sin[4x + (n+.2)/ Pi])/2,{n,0,19}]
}]
],{x,0,2 Pi},
PlotPoints->200,
DisplayFunction->Identity,
 Axes->None]&/@{PolarPlot,Plot}
]]

V6

With[{max=19},
GraphicsRow[#[Evaluate[Flatten[{
Table[(1.2 +.4 Sin[3 x +.5]) +((4 + Sin[5 x]) - (1.2+.4 Sin[3 x +.5]))(1+Sin[3 x + (n +  .2 Sin[100 x])/ Pi])/2,{n,0,max}],
Table[(4 + Sin[5 x]) +((7 + Sin[7 x]) - (4+ Sin[5 x])) (1+Sin[5 x + n/ Pi])/2,{n,0,max}],
Table[(7 + Sin[7 x]) +((10 + Sin[4 x +4.7]) - (7+ Sin[7 x])) (1+Sin[4 x + n/ Pi])/2,{n,0,max}],
Table[(7 + Sin[7 x]) +((10+ Sin[4 x + 4.7]) - (7+ Sin[7 x])) (1+Sin[4x + (n+.2)/ Pi])/2,{n,0,max}]
}]
],{x,0,2 Pi}, Axes->None,PlotStyle->Directive[Black,Thin]]&/@{PolarPlot,Plot}
]
]