Wolfram Language

Algèbre et théorie des nombres

Modélisation de phyllotaxie

L'angle d'or est l'angle qui divise un angle complet en deux parties conformément au nombre d'or.

Extrayez la valeur de l'angle d'or.

In[1]:=
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FunctionExpand[GoldenAngle]
Out[1]=

Approximez la valeur en radians et en degrés.

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

L'angle d'or peut être utilisé pour modéliser les motifs de phyllotaxie.

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Définissez une fonction de phyllotaxie en utilisant GoldenAngle.

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phyllotaxis[step_] := Table[Sqrt[i] AngleVector[i GoldenAngle], {i, 0, 1000, step}]

Utilisez Graphics pour générer un motif de phyllotaxie à partir de ces points.

In[5]:=
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Graphics[{PointSize[Medium], Point[phyllotaxis[1]]}]
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Mettez en évidence des spirales de différentes étapes en utilisant différentes couleurs.

In[6]:=
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Graphics[{PointSize[Medium], RGBColor[ 0.2980392156862745, 0.28627450980392155`, 0.5490196078431373], Point[phyllotaxis[1]], GrayLevel[1], Point[phyllotaxis[5]]}]
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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]]}]
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Les motifs de phyllotaxie peuvent également être trouvés dans les têtes de tournesol.

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BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSize->Automatic, ImageSizeRaw->{300, 200}, PlotRange->{{0, 300}, {0, 200}}]\)

Definissez un motif.

In[9]:=
Click for copyable input
motif = FilledCurve@ BSplineCurve[4 {{0, -.75}, {0, .75}, {1, 0}, {1, 0}}, SplineClosed -> True];

Visualisez-le.

In[10]:=
Click for copyable input
Graphics[motif]
Out[10]=

Construisez une tête de tournesol à partir de celui-ci.

In[11]:=
Click for copyable input
Graphics[{EdgeForm[ GrayLevel[1]], Table[Rotate[Translate[motif, {Sqrt[i], 0}], i GoldenAngle, {0, 0}], {i, 100, 0, -1}]}]
Out[11]=

Exemples connexes

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