잎차례 모델링
황금 각도는 전체의 각도를 황금 비율로 주어지는 것과 같이 두 부분으로 나누는 각입니다.
황금 각도의 정확한 값을 구합니다.
In[1]:=
FunctionExpand[GoldenAngle]
Out[1]=
라디안과 도의 값을 근사합니다.
In[2]:=
N@{GoldenAngle, GoldenAngle/Degree}
Out[2]=
황금 각은 잎차례 패턴 모델링에 사용할 수 있습니다.
Out[3]=
GoldenAngle를 사용하여 잎차례 함수를 정의합니다.
In[4]:=
phyllotaxis[step_] :=
Table[Sqrt[i] AngleVector[i GoldenAngle], {i, 0, 1000, step}]
Graphics를 사용하여 이러한 점에서 잎차례 패턴을 생성합니다.
In[5]:=
Graphics[{PointSize[Medium], Point[phyllotaxis[1]]}]
Out[5]=
다른 색상을 사용하여 다른 단계의 나선을 강조합니다.
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]=
잎차례 패턴은 해바라기 꽃에서도 볼 수 있습니다.
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}}]\)
모티브를 정의합니다.
In[9]:=
motif = FilledCurve@
BSplineCurve[4 {{0, -.75}, {0, .75}, {1, 0}, {1, 0}},
SplineClosed -> True];
시각화합니다.
In[10]:=
Graphics[motif]
Out[10]=
이제 해바라기 꽃을 구축합니다.
In[11]:=
Graphics[{EdgeForm[
GrayLevel[1]],
Table[Rotate[Translate[motif, {Sqrt[i], 0}],
i GoldenAngle, {0, 0}], {i, 100, 0, -1}]}]
Out[11]=