Plot Fibonacci Sequence (with tikzpicture)

Question

How do I plot the Fibonacci sequence (using tikzpicture preferably)?

\documentclass{article}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[xmin=0, xmax=30, ymin=2, ymax=3]
    \addplot[samples at={1,2,...,30}, only marks] expression {<Add Fibonacci sequence here>};
  \end{axis}
\end{tikzpicture}

\end{document}

Edit

Since it seems more complicated than I thought, I went for the following solution: plot the discrete version of the continuous Fibonacci function, see for instance here. Any suggestions are surely still welcomed.

So now it goes like this:

\documentclass{article}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[xmin=0, xmax=8, ymin=0, ymax=14, xlabel=$n$, ylabel=$a_n$, axis x line=center, axis y line=center]
    \addplot[samples at={0,1,...,7},only marks] expression {( ((1+sqrt(5))/(2))^\x - cos(deg(\x * pi)) * ((1+sqrt(5))/(2))^(-\x) )/sqrt(5) };
  \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

Here is a direct loop method :

\documentclass[tikz,border=7pt]{standalone}
\begin{document}
  \tikz
    \foreach[
        remember=\g as \h (initially 1),
        remember=\f as \g (initially 0),
        evaluate=\f using int(\g+\h)
      ] \n in {1,...,7}
      \fill[green,draw=black] (\n,0) rectangle +(1,\f) node[black,scale=2,above left]{\f};
\end{document}

EDIT: If you want to go to 30 (and more) you can use xint package.

\documentclass[tikz,border=7pt]{standalone}
\usepackage{xintexpr}
\begin{document}
  \begin{tikzpicture}[xscale=.35]
    \foreach[
        remember=\g as \h (initially 1),
        remember=\f as \g (initially 0)
      ] \n in{1,...,30}{
        \edef\f{\thexintexpr \g + \h \relax}
        \edef\ff{\thexintfloatexpr \f/10000 \relax}
        \fill[green,draw=black] (\n,0) rectangle +(1,\ff);
      }
  \end{tikzpicture}
\end{document}

EDIT: Following the comment of @jfbu the following code will produce the same image:

\documentclass[tikz,border=7pt]{standalone}
\usepackage{xintexpr}
\begin{document}
  \xdef\fibs{\thexintfloatexpr rrseq(0, 1/10000 ; @1+@2, i=2..30)\relax}
  \tikz[xscale=.35]
    \foreach[count=\n] \f in \fibs
      \fill[green,draw=black] (\n,0) rectangle +(1,\f);
\end{document}

NOTE: It is probably faster to use directly something like

\foreach[count=\n] \f in {1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040}{
  ...
}

Answer 2

The Fibonacci series is implemented in the pgfmanual in section 56.1. All you need to do is to adapt it from there.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{math}
\begin{document}

\tikzmath{
% Adapted from http://www.cs.northwestern.edu/academics/courses/110/html/fib_rec.html 
function fibonacci(\n) {
    if \n == 0 then {
      return 0;
    } else {
       return fibonacci2(\n, 0, 1);
}; };
  function fibonacci2(\n, \p, \q) {
    if \n == 1 then {
      return \q;
    } else {
      return fibonacci2(\n-1, \q, \p+\q);
    };
  };
}
\begin{tikzpicture}
\foreach \X in {0,1,...,8}{
\node[circle,fill,label=above:{\pgfmathparse{int(fibonacci(\X))}
\pgfmathresult}] at (\X,{fibonacci(\X)})  {};}

\end{tikzpicture}
\end{document}

ADDITIONAL REMARK: It turns out not to be so easy to plot this function with pgfplots. The problem seems to be that pgfplots uses the fpu library (yet setting \pgfkeys{/pgf/fpu=false} does not help). In this answer, the problem is avoided by doing an external computation. However, I wrote the answer when there was no MWE available, and followed the directive "using tikzpicture preferably" ;-).

Answer 3

With a variant of https://tex.stackexchange.com/a/51422/4427, we can generate the sequence to be fed to \foreach:

\documentclass[tikz]{standalone}
\usepackage{xparse}

\ExplSyntaxOn
\cs_new:Npn \fibo #1 { \fibo_recurrence:nnnn{0}{1}{0}{#1} }
\cs_new:Npn \fibo_recurrence:nnnn #1 #2 #3 #4
 {
  \int_compare:nTF { #1 = #4 }
  { #3 }
  {
   #3 , \fibo_recurrence:ffnn
      { \int_eval:n {#1+1} }
      { \int_eval:n {#2+#3} }
      { #2 }
      { #4 }
  }
 }
\cs_generate_variant:Nn \fibo_recurrence:nnnn { ffnn }
\ExplSyntaxOff

\begin{document}

\begin{tikzpicture}
\edef\fibos{\fibo{7}}
\foreach [count=\index] \f in \fibos
 {
  \fill[green,draw=black] (\index,0) rectangle +(1,\f) 
    node[black,scale=2,above left]{\f};
 }
\end{tikzpicture}

\end{document}