Phyllotaxis modellieren
Der goldene Winkel ist jener Winkel, der einen Winkel von  im Verhältnis des  goldenen Schnitts in zwei Teile teilt.
 im Verhältnis des  goldenen Schnitts in zwei Teile teilt.
Der exakte Wert des goldenen Winkels.
In[1]:=

FunctionExpand[GoldenAngle]Out[1]=

Der ungefähre Wert in Radianten und Graden.
In[2]:=

N@{GoldenAngle, GoldenAngle/Degree}Out[2]=

Mit dem goldenen Winkel können Phyllotaxis-Muster modelliert werden.
Out[3]=

Definieren Sie eine Phyllotaxis-Funktion mithilfe von GoldenAngle.
In[4]:=

phyllotaxis[step_] := 
 Table[Sqrt[i] AngleVector[i GoldenAngle], {i, 0, 1000, step}]Verwenden Sie Graphics, um ein Phyllotaxis-Muster aus diesen Punkten zu erstellen.
In[5]:=

Graphics[{PointSize[Medium], Point[phyllotaxis[1]]}]Out[5]=

Heben Sie Spiralen unterschiedlicher Schritte in verschiedenen Farben hervor.
In[6]:=

Graphics[{PointSize[Medium], RGBColor[
  0.2980392156862745, 0.28627450980392155`, 0.5490196078431373], 
  Point[phyllotaxis[1]], GrayLevel[1], Point[phyllotaxis[5]]}]Out[6]=

In[7]:=

Graphics[{PointSize[Medium], LCHColor[
Rational[1, 2], 
Rational[1, 2], 
Rational[1, 3]], Point[phyllotaxis[1]], CMYKColor[0, 0, 1, 0.05], 
  Point[phyllotaxis[7]]}]Out[7]=

Phyllotaxis-Muster findet man auch in Köpfen von Sonnenblumen.
In[8]:=

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"], {{0, 200}, {300, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{300, 200},
PlotRange->{{0, 300}, {0, 200}}]\)Bestimmen Sie ein Motiv.
In[9]:=

motif = FilledCurve@
   BSplineCurve[4 {{0, -.75}, {0, .75}, {1, 0}, {1, 0}}, 
    SplineClosed -> True];Visualisieren Sie es.
In[10]:=

Graphics[motif]Out[10]=

Konstruieren Sie daraus einen Sonnenblumenkopf.
In[11]:=

Graphics[{EdgeForm[
GrayLevel[1]],
  Table[Rotate[Translate[motif, {Sqrt[i], 0}], 
    i GoldenAngle, {0, 0}], {i, 100, 0, -1}]}]Out[11]=

















 
  
  
  
  
  
  
 