From bdd80b972f0e79d0832f83250875a2c863db6ec7 Mon Sep 17 00:00:00 2001 From: ulaulaman Date: Wed, 2 Dec 2020 22:08:07 +0100 Subject: [PATCH] The butterfly curve --- math/butterfly.tex | 36 ++++++++++++++++++++++++++++++++++++ math/pdf/butterfly.pdf | Bin 0 -> 105153 bytes 2 files changed, 36 insertions(+) create mode 100755 math/butterfly.tex create mode 100644 math/pdf/butterfly.pdf diff --git a/math/butterfly.tex b/math/butterfly.tex new file mode 100755 index 0000000..8eee05c --- /dev/null +++ b/math/butterfly.tex @@ -0,0 +1,36 @@ +\documentclass{standalone} +\usepackage{tikz} +\usepackage{pgfplots} +\pgfplotsset{width=7cm,compat=1.8} +\usepgfplotslibrary{polar} + +\title{Butterfly curve} +\begin{document} + \begin{tikzpicture} + \def\a{1} + \def\b{4} + \def\c{12} + \def\A{2} + \def\B{5} + \def\pig{3.14} + % + \begin{scope} + \node at (2.5,0) {The Butterfly curve: Fay's polar equation}; + \end{scope} + % + \begin{scope}[shift={(0,-6.5)}] + \begin{polaraxis}[grid=none,hide y axis] + \addplot+[mark=none,domain=0:3600,samples=2000] {e^cos(\a * x)-\A * cos(\b * x) + (sin(x / \c))^\B}; + \end{polaraxis} + \node at (2.5,-1) {$\rho = e^{\cos \vartheta} - 2 \cos (4 \theta) + \sin^5 (\vartheta / 12)$}; + \end{scope} + % + \begin{scope}[shift={(0,-15)}] + \node at (2.5,6.5) {The Butterfly curve: Geum and Kim's equation}; + \begin{polaraxis}[grid=none,hide y axis] + \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}; + \end{polaraxis} + \node at (2.5,-1) {$\rho = e^{\sin \vartheta} - 2 \cos (4 \theta) + \sin^5 \left ( \frac{2\vartheta -\pi}{24} \right )$}; + \end{scope} + \end{tikzpicture} +\end{document} \ No newline at end of file diff --git a/math/pdf/butterfly.pdf b/math/pdf/butterfly.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9fadbd44de0dfda32a8ffda2c151f2a90403fca0 GIT binary patch literal 105153 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