pgfplots add tag
JeT
I'd like to replace the mark of my plot with a mini brownian diffusion. 

I'll probably need to embed it in a `pic`.

I have the ingredients, I need a little help (some would say I am missing a pi(e)c(e)... ) on the recipe.

I don't look for the version below with one brownian  replicated 5 times and not consistent  with the measure on the main graph.

![MAinplot2.png](/image?hash=545e69920b248944cf8f79ba2abee0d2bd7bcf1be3ecfb4e724fba8e371ae384)

I imagine more something like (Poorly copied pasted) with one brownian per period, whose coordinates are consistent with the main plot.

![TAPic000.png](/image?hash=c45665aaad7f9cab50f178befe5b346433c671cd3c8585b7411954ef0a0ff929)

**Where do I need help ?**

I'd like each brownian 
 - to start at the mark 
 - have a width of one tick for the pic
 - diffusion being consistent with the main plot grid


Details in the MWE below.

```
\documentclass[tikz]{standalone}
\usepackage{pgfplots, pgfplotstable}
\usetikzlibrary{positioning}

\tikzset{
	declare function={
 	invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));
 }
} 

%-----------------------------------------------------------------
% Code from Jake @ TeX.SE to generate brownian motions
% If you have an idea to load to improve the compilation time
\makeatletter
\pgfplotsset{
 table/.cd,
 brownian motion/.style={
  create on use/brown/.style={
   create col/expr accum={
 (\coordindex>0)*(
  max(
   min(
 invgauss(rnd,rnd)*0.25*sqrt(1)+\pgfmathaccuma,
 \pgfplots@brownian@max
   ),
   \pgfplots@brownian@min
  )
 ) + (\coordindex<1)*\pgfplots@brownian@start
   }{\pgfplots@brownian@start}
  },
  y=brown, x expr={\coordindex},
  brownian motion/.cd,
  #1,
  /.cd
 },
 brownian motion/.cd,
   min/.store in=\pgfplots@brownian@min,
  min=-inf,
   max/.store in=\pgfplots@brownian@max,
   max=inf,		
   start/.store in=\pgfplots@brownian@start,
  start= 0 
}
\makeatother

%-----------------------------------------------------------------
% Create the pic that generates brownian motions
% I did my homework and read the pgfmanual.
% It enabled me to use parameters in `pic`
% The idea is to have flexibility on the brownian
% \pic{BM=color/Starting@y/nbs of paths/nbs of points in the path};
% "nbs of points in the path" represents the subdivision of 1 unit of time

\tikzset{pics/BM/.style args={#1/#2/#3/#4}{
code = {%
\pgfmathsetseed{3}
\pgfplotstablenew{#4}\wiener % Initialise an empty table with #4 steps for brownians
\node[](#1){
\begin{tikzpicture}
 \begin{axis}[
   axis line style={draw=none},
   tick style={draw=none},  
   xtick=\empty, ytick=\empty,
 % xlabel = subdivision of 1 unit of time,
 % ylabel = $S$,
 	]
 	\foreach \i in {1,...,#3}{% <- I can draw #3 paths
	% start is a paramater to make it start at the mark  on the main plot 	
 	\addplot[#1,smooth] table [brownian motion={start=#2}] {\wiener};
% 	\addplot[#1,smooth] table 
%	[brownian motion={start=#2,min=80,max=120}] {\wiener};
% no impact of min and max...	
 	}
 \end{axis}
\end{tikzpicture}
};
}}}


\begin{document}

% Main plot
\begin{tikzpicture}
	\begin{axis}[
 	xlabel = time,
 	ylabel = $S$
 ]
 
 %I'll apply it to a function later
 % \addplot+[domain=0:5] {f(x)}; 
 % But as a start, I set the list of points manually
 \addplot[color=blue,smooth,mark=*] coordinates {
 	(0,100)
 	(1,102)
 	(2,95)
 	(3,101)
 	(4,105)
 	(5,98)
 };

	\end{axis}
\end{tikzpicture}

% I'll display one consistent type
\begin{tikzpicture}
	\pic{BM=orange/100/10/200};	% First point 
\end{tikzpicture}
\begin{tikzpicture}
	\pic{BM=green/102/10/200};	% Second point
\end{tikzpicture}
\begin{tikzpicture}
	\pic{BM=blue/95/10/200}; % Third point
\end{tikzpicture}
\begin{tikzpicture}
	\pic{BM=orange/101/10/200};	% Fourth point
\end{tikzpicture}

	\end{document}
```
Top Answer
marmot
This is an answer that literally uses `pic`s as plot marks. The `pic` has various options which I hope are somewhat selfexplanatory. Please note that generally you will be better off if you dial a rather recent compatibility mode of `pgfplots`. I chose `\pgfplotsset{compat=1.17}` and there is no guarantee that the following works with ancient versions. To make a `pic` a plot mark, one can use something of the sort
```
\pgfdeclareplotmark{Brownian}{\pic[every mark]{Brownian};}
```
The `every mark` key is used to allow the user to pass styles to the `pic` using the `mark options` key, so this works just like any other plot mark. The `axis direction cs:` prefix is crucial to have  reasonable pics inside an `axis` environment. This also means that you cannot use them outside an `axis` unless you take extra steps, see the PS below for one out of several options to accomplish this. Finally, we use `scatter classes` to define different plot marks with different `mark options`, they can then simply be added in square brackets after the coordinates, as the following example illustrates.
```
\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\tikzset{pics/Brownian/.style={code={
	\tikzset{Brownian/.cd,#1}%
    \def\pv##1{\pgfkeysvalueof{/tikz/Brownian/##1}}%
	\foreach \XXX in {1,...,\pv{N}}	
	{
	\draw[pic actions] (axis direction cs:0,0) 
	foreach \YYY in {1,...,\pv{M}} 
	{-- ++ (axis direction cs:{\pv{dx}},{\pv{dy}*(rnd-0.5)})}
	;}
	}},Brownian/.cd,N/.initial=25,M/.initial=25,dx/.initial=0.04,dy/.initial=0.25}
\begin{document}

\pgfdeclareplotmark{Brownian}{\pic[every mark]{Brownian};}

% Main plot
\begin{tikzpicture}
	\begin{axis}[xmax=6,
	scatter/classes={
        a={mark=Brownian,mark options={red,Brownian/dy=0.4,Brownian/N=40}},
        b={mark=Brownian,mark options={blue}},
        c={mark=Brownian,mark options={orange,Brownian/dy=0.12}}
},
 	xlabel = time,
 	ylabel = $S$
 ]
 \addplot[color=blue,smooth, scatter,
        scatter src=explicit symbolic,] coordinates {
 	(0,100) [c]
 	(1,102) [b]
 	(2,95) [a]
 	(3,101) [a]
 	(4,105) [b]
 	(5,98) [c]
 };
\end{axis}
\end{tikzpicture}
\end{document}
```
![Screen Shot 2021-02-21 at 10.52.46 AM.png](/image?hash=7aeff7d1ef95bef48985ec906bf564c4cab8eb838254ac75ff932837d1e566e7)

P.S. If one wants to create a `pic` that works inside *and* outside of an `axis` environment, one can use the `\pgfplotsifinaxis` macro. There are other options available, but since this is not central to the current question I won't spell them out since I did not test any of them.
```
\tikzset{pics/Brownian/.style={code={
	\tikzset{Brownian/.cd,#1}%
    \def\pv##1{\pgfkeysvalueof{/tikz/Brownian/##1}}%
	\foreach \XXX in {1,...,\pv{N}}	
	{\pgfplotsifinaxis{%
	\draw[pic actions] (axis direction cs:0,0) 
	foreach \YYY in {1,...,\pv{M}} 
	{-- ++ (axis direction cs:{\pv{dx}},{\pv{dy}*(rnd-0.5)})};}{%
	\draw[pic actions] (0,0) 
	foreach \YYY in {1,...,\pv{M}} 
	{-- ++ ({\pv{dx}},{\pv{dy}*(rnd-0.5)})};}{%	
	}}
	}},Brownian/.cd,N/.initial=25,M/.initial=25,dx/.initial=0.04,dy/.initial=0.25}
```

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