Generating consistently formatted random plots in pgfplot/tikz

Question

I have some code that will generate a new plot based on a random number. I'm having issues formatting the tick labels, however.

A few things I want to achieve:

1. The y-tick label should always start at \N.
2. I would always like 5 major ticks in the x and y axis.
3. The gridlines/ticks should stop after the 5th major x/y tick but the axis arrow should continue for a small distance longer.
4. The plot is rendering ".1.1" in the bottom left hand corner, which I want to get rid of.

Here is my MWE:

\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{pgf}
\usetikzlibrary{calc}
\pgfplotsset{compat=1.11}

\begin{document}
\pgfmathsetmacro\N{random(1,1000)}
\pgfmathsetmacro\HL{random(0.1, 10)}
\begin{tikzpicture}

\begin{axis}[
xmin=0, xmax=5*\HL+0.1*\HL,
ymin=0, ymax=\N+0.1*\N,    
restrict y to domain=0:\N,
smooth,
samples = 20,
grid=both,
grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!50},
axis lines=middle,
minor tick num=10,
axis line style={-latex},
ticklabel style={font=\tiny,fill=white},
]

\addplot[domain=0:5*\HL]  {\N*pow(0.5, x/\HL)};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

If I understand you correctly, you do not want nice numbers for your tick marks (which would be much harder). Also, I had a problem with the FPU version of random(), so I created my own.

Note: Tikz does not as a rule run key options through \pgfmathparse, so at least there you need to put all math operations and even simple macros inside braces.

\documentclass{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows.meta}
\pgfplotsset{compat=1.11}

\begin{document}
\tikzset{/pgf/declare function={myrandom(\a,\b)=\a+(\b-\a)*rnd;}}%
\pgfmathsetmacro\N{myrandom(1,1000)}%
\pgfmathsetmacro\HL{myrandom(0.1, 10)}%
\begin{tikzpicture}

\xdef\ylist{0.0}
\foreach \i in {0.2,0.4,0.6,0.8,1.0} {%
  \pgfmathparse{\i*\N}%
  \xdef\ylist{\ylist,\pgfmathresult}%
}
\xdef\xlist{0.0}
\foreach \i in {1,2,3,4,5} {%
  \pgfmathparse{\i*\HL}%
  \xdef\xlist{\xlist,\pgfmathresult}%
}
\begin{axis}[name=border,
xmin=0, xmax={5*\HL},
ymin=0, ymax={\N},    
%restrict y to domain=0:{\N},% not needed
ytick={\ylist},
xtick={\xlist},
smooth,
samples = 20,
grid=both,
grid style={line width=.1pt, draw=gray!10},
major grid style={line width=.2pt,draw=gray!50},
axis lines=middle,
minor tick num=10,
axis line style={-Butt Cap},
ticklabel style={font=\tiny,fill=white},
]
\addplot[domain=0:{5*\HL}]  {\N*pow(0.5, x/\HL)};
\end{axis}
\draw[-latex] (border.south east) -- +(5mm,0pt);
\draw[-latex] (border.north west) -- +(0pt,5mm);
\end{tikzpicture}
\end{document}