Curlicue Fractal

Author

Eric W. Weisstein
January 5, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Fractals/CurlicueFractal.nb.

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

©2010 Wolfram Research, Inc. except for portions noted otherwise

Code

Curlicue[s_,n_Integer:10000,opts___?OptionQ]:=
Graphics[
Line[FoldList[Plus,{0.,0.},Through[{Cos,Sin}[#]]&/@FoldList[Plus,0.,2Pi s Range[n]]]],
opts,AspectRatio->Automatic,PlotRange->All
]

Definition

δ=4.66920160910299067185320382046620161725818557747576863274565134300413433021131473713868974402394801381716;

First[RealDigits[δ]]//Length

Examples

V5

<<Utilities`Typesetting`

Show[
GraphicsArray[
Partition[
Curlicue[#,10000,PlotLabel->TraditionalForm[HoldForm[#]]]&/@
{
GoldenRatio,Log[2],E,Sqrt[2],EulerGamma,Pi,Unevaluated[δ]
},
3,3,{1,1},{}]
]
]//Timing

V6

GraphicsGrid[
Partition[
Curlicue[#,10000,PlotLabel->TraditionalForm[HoldForm[#]]]&/@
{
GoldenRatio,Log[2],E,Sqrt[2],EulerGamma,Pi,Unevaluated[δ]
},
3,3,{1,1},{}]
]