36 lines
1.1 KiB
TeX
36 lines
1.1 KiB
TeX
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\documentclass{standalone}
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\usepackage{tikz}
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\usepackage{pgfplots}
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\pgfplotsset{width=7cm,compat=1.8}
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\usepgfplotslibrary{polar}
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\title{Butterfly curve}
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\begin{document}
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\begin{tikzpicture}
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\def\a{1}
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\def\b{4}
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\def\c{12}
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\def\A{2}
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\def\B{5}
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\def\pig{3.14}
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%
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\begin{scope}
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\node at (2.5,0) {The Butterfly curve: Fay's polar equation};
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\end{scope}
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%
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\begin{scope}[shift={(0,-6.5)}]
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\begin{polaraxis}[grid=none,hide y axis]
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\addplot+[mark=none,domain=0:3600,samples=2000] {e^cos(\a * x)-\A * cos(\b * x) + (sin(x / \c))^\B};
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\end{polaraxis}
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\node at (2.5,-1) {$\rho = e^{\cos \vartheta} - 2 \cos (4 \theta) + \sin^5 (\vartheta / 12)$};
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\end{scope}
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%
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\begin{scope}[shift={(0,-15)}]
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\node at (2.5,6.5) {The Butterfly curve: Geum and Kim's equation};
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\begin{polaraxis}[grid=none,hide y axis]
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\addplot+[mark=none,domain=0:3600,samples=2000,color=red] {e^sin(\a * x)-\A * cos(\b * x) + (sin((2*x - \pig)/ (2*\c)))^\B};
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\end{polaraxis}
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\node at (2.5,-1) {$\rho = e^{\sin \vartheta} - 2 \cos (4 \theta) + \sin^5 \left ( \frac{2\vartheta -\pi}{24} \right )$};
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\end{scope}
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\end{tikzpicture}
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\end{document}
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