diff options
Diffstat (limited to 'buch/chapters/040-rekursion/images/fibonacci.tex')
| -rw-r--r-- | buch/chapters/040-rekursion/images/fibonacci.tex | 149 |
1 files changed, 149 insertions, 0 deletions
diff --git a/buch/chapters/040-rekursion/images/fibonacci.tex b/buch/chapters/040-rekursion/images/fibonacci.tex new file mode 100644 index 0000000..3bd8b63 --- /dev/null +++ b/buch/chapters/040-rekursion/images/fibonacci.tex @@ -0,0 +1,149 @@ +% +% fibonacci.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\input{fibonaccigrid.tex} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\achsen{ + \draw[->] (-2.1,0) -- (10.8,0) + coordinate[label={$\operatorname{Re}F(z)$}]; + \draw[->] (0,-2.6) -- (0,2.7) + coordinate[label={right:$\operatorname{Im}F(z)$}]; + \node at (10.8,2.7) {$\mathbb{C}$}; +} + +\def\zahl#1#2{ + \fill[color=white,opacity=0.8] + ({#1-0.65},-0.6) rectangle ({#1+0.65},-0.2); + \node[color=darkgreen] at (#1,-0.43) {$#2\mathstrut$}; +} + +\draw[color=gray!20,line width=2.0pt] (-2,3.2) -- (11.3,3.2); + +\def\topskala{1.55} + +\draw[->,color=darkgreen!30,line width=5pt] + ({-0.2*\topskala},4.3) to[out=-120,in=120] (-0.1,0.2); +\draw[->,color=darkgreen!30,line width=5pt] + ({0.9*\topskala},4.3) to[out=-110,in=70] (0.9,-5.1); +\draw[->,color=darkgreen!30,line width=5pt] + ({2.0*\topskala},4.3) to[out=-90,in=76] (1.0,-10.6); + +\draw[->,color=darkgreen!30,line width=5pt] + ({3.0*\topskala},4.3) to[out=-90,in=90] (2.0,0.2); +\draw[->,color=darkgreen!30,line width=5pt] + ({3.9*\topskala},4.3) to[out=-110,in=80] (3.0,-5.3); +\draw[->,color=darkgreen!30,line width=5pt] + ({4.8*\topskala},4.3) to[out=-120,in=90] (5.0,-10.8); + +\draw[->,color=darkgreen!30,line width=5pt] + ({6.0*\topskala},4.3) to[out=-90,in=70] (8.1,0.2); + + +\begin{scope}[yshift=4.8cm,scale=\topskala] + + \draw[->] (-0.7,0) -- (6.8,0) + coordinate[label={$\operatorname{Re}z$}]; + \draw[->] (0,-0.7) -- (0,0.8) + coordinate[label={right:$\operatorname{Im}z$}]; + \foreach \x in {-0.5,-0.4,...,6.501}{ + \draw[color=gray,line width=0.1pt] (\x,-0.5) -- (\x,0.5); + } + \foreach \y in {-0.5,-0.4,...,0.501}{ + \draw[color=gray,line width=0.1pt] (-0.5,\y) -- (6.5,\y); + } + + \foreach \n in {0,3,6}{ + \foreach \x in {-0.5,-0.4,...,0.501}{ + \draw[color=blue,line width=0.7pt] + ({\n+\x},-0.5) -- ({\n+\x},0.5); + } + \foreach \y in {-0.5,-0.4,...,0.501}{ + \draw[color=red,line width=0.7pt] + ({\n-0.5},\y) -- ({\n+0.5},\y); + } + } + \foreach \n in {0,...,6}{ + \fill[color=white,opacity=0.8] + ({\n-0.1},-0.28) rectangle ({\n+0.1},-0.05); + \node[color=darkgreen] at (\n,0) [below] {$\n$}; + \fill[color=darkgreen] (\n,0) circle[radius=0.05]; + \fill[color=white] (\n,0) circle[radius=0.02]; + } + + \node at (6.8,0.8) {$\mathbb{C}$}; + +\end{scope} + +\begin{scope}[scale=1] + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibgrid + \end{scope} + \achsen + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibzero + \fibthree + \fibsix + \end{scope} + \fibcurve + \node[color=magenta] at (-1.3,-1.8) {$n=0$}; + \node[color=magenta] at (1.9,0.8) {$n=3$}; + \node[color=magenta] at (8,2.3) {$n=6$}; + \zahl{0}{F(0)=0} + \zahl{2}{F(3)=2} + \zahl{8}{F(6)=8} +\end{scope} + +\begin{scope}[yshift=-5.5cm,scale=1] + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibgrid + \end{scope} + \achsen + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibone + \fibfour + \end{scope} + \fibcurve + \node[color=magenta] at (1,1.2) {$n=1$}; + \node[color=magenta] at (3,1.1) {$n=4$}; + \zahl{1}{F(1)=1} + \zahl{4}{F(4)=3} +\end{scope} + +\begin{scope}[yshift=-11cm,scale=1] + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibgrid + \end{scope} + \achsen + \begin{scope} + \clip (-2,-2.6) rectangle (10.5,2.6); + \fibtwo + \fibfive + \end{scope} + \fibcurve + \node[color=magenta] at (0.7,1.1) {$n=2$}; + \node[color=magenta] at (5,1.5) {$n=5$}; + \zahl{2}{F(2)=1} + \zahl{5}{F(5)=5} +\end{scope} + +\end{tikzpicture} +\end{document} + |