Wolfram 언어

대수학과 정수론

잎차례 모델링

황금 각도는 전체의 각도를 황금 비율로 주어지는 것과 같이 두 부분으로 나누는 각입니다.

황금 각도의 정확한 값을 구합니다.

In[1]:=
Click for copyable input
FunctionExpand[GoldenAngle]
Out[1]=

라디안과 도의 값을 근사합니다.

In[2]:=
Click for copyable input
N@{GoldenAngle, GoldenAngle/Degree}
Out[2]=

황금 각은 잎차례 패턴 모델링에 사용할 수 있습니다.

Out[3]=

GoldenAngle를 사용하여 잎차례 함수를 정의합니다.

In[4]:=
Click for copyable input
phyllotaxis[step_] := Table[Sqrt[i] AngleVector[i GoldenAngle], {i, 0, 1000, step}]

Graphics를 사용하여 이러한 점에서 잎차례 패턴을 생성합니다.

In[5]:=
Click for copyable input
Graphics[{PointSize[Medium], Point[phyllotaxis[1]]}]
Out[5]=

다른 색상을 사용하여 다른 단계의 나선을 강조합니다.

In[6]:=
Click for copyable input
Graphics[{PointSize[Medium], RGBColor[ 0.2980392156862745, 0.28627450980392155`, 0.5490196078431373], Point[phyllotaxis[1]], GrayLevel[1], Point[phyllotaxis[5]]}]
Out[6]=
In[7]:=
Click for copyable input
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]:=
Click for copyable input
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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}}]\)

모티브를 정의합니다.

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

시각화합니다.

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

이제 해바라기 꽃을 구축합니다.

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]=

관련 예제

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