Basic Examples (4)
Basic Examples
(4)
Four steps for Koch quadratic rules:
In[49]:=
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———
Get just the resulting string after only one step:
In[50]:=
Last[SubstitutionSystem[{"F""FF-F-F-F-F-F+F"},"F-F-F-F",1]]
Out[50]=
FF-F-F-F-F-F+F-FF-F-F-F-F-F+F-FF-F-F-F-F-F+F-FF-F-F-F-F-F+F
———
Continuously modify the angle:
In[51]:=
Animate[{"F""-F+F-F-F+F+FF-F+F+FF+F-F-FF+FF-FF+F+F-FF-F-F+FF-F-F+F+F-F+"},"F+F+F+F",1,nDegree,ColorFunctionColorData["RedBlueTones"]],{n,30.,120.}
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———
Grid for named fractals:
In[59]:=
lsystems={{"32-segment curve",{"F""-F+F-F-F+F+FF-F+F+FF+F-F-FF+FF-FF+F+F-FF-F-F+FF-F-F+F+F-F+"},"F+F+F+F",2,90},{"box fractal",{"F""F-F+F+F-F"},"F-F-F-F",3,90},{"dragon curve",{"X""X+YF+","Y""-FX-Y"},"FX",10,90},{"Hilbert curve",{"L""+RF-LFL-FR+","R""-LF+RFR+FL-"},"L",4,90},{"Hilbert curve II",{"X""XFYFX+F+YFXFY-F-XFYFX","Y""YFXFY-F-XFYFX+F+YFXFY"},"X",3,90},{"Koch snowflake",{"F""F+F--F+F"},"F--F--F",3,60},{"Peano curve",{"F""F+F-F-F-F+F+F+F-F"},"F",2,90},{"Peano-Gosper curve",{"X""X+YF++YF-FX--FXFX-YF+","Y""-FX+YFYF++YF+FX--FX-Y"},"FX",3,60},{"quadratic Koch island",{"F""F-F+F+FFF-F-F+F"},"F+F+F+F",2,90},{"Sierpiński arrowhead",{"X""YF+XF+Y","Y""XF-YF-X"},"YF",5,60},{"Sierpiński curve",{"X""XF-F+F-XF+F+XF-F+F-X"},"F+XF+F+XF",3,90},{"Siepiński sieve",{"F""FF","X""--FXF++FXF++FXF--"},"FXF--FF--FF",4,60}};
In[61]:=
GraphicsGridPartition[Sequence@@(Take[#,{2,-2}]),Last[#]Degree//N,PlotLabelFirst[#],BaseStyle{FontFamily->"Times",FontSlant->"Italic"}]&/@lsystems,4,ImageSize600
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Options (2)
Options
(2)
Applications (3)
Applications
(3)