Arbitrary Ragged Curves for Phase Diagram in TikZ

Question

How can one draw a good looking curved random line extending along a diagonal connecting two arbitrary nodes in TikZ?

(Also, how do I add arrowheads like I would usually do, or do I have to create an arrowhead at a point and superpose it over the endpoint, separately?)

(There are some idea on how to do a good looking vertical line or horizontal line in this topic Drawing randomly ragged lines in technical drawings . Please use the MWE from there.

\documentclass[12pt]{article} % SIZE OF FONT AND ITS LAYOUT ON EACH PAGE.
\usepackage[top = 1in, bottom = 1in, left = 1in, right = 1in]{geometry}
\usepackage{amsmath, booktabs, graphicx, setspace}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz,tkz-graph,tikz-cd} % DIAGRAMS.
\usetikzlibrary{arrows, calc, decorations.markings}
\usetikzlibrary{calc}

\newcommand\irregularline[2]{%
    let \n1 = {(rand*(#1)} in
    +(0,\n1)
    \foreach \a in {0.1,0.2,...,#2}{
    let \n1 = {rand*(#1)} in
    -- +(\a,\n1)
    }}  % #1=seed, #2=length of horizontal line

% This is code for a horizontal random line that I like.
% How to make this sort of line connect two arbitrary points, 
% and perhaps, how to make it curve in a natural way?

\begin{document}

\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=1.8,auto]

% replace with randomly ragged line that curves 

\draw [-,line width=1pt] (0,0) edge (3,3);

\end{tikzpicture}
\end{center}
\caption{CAPTION GOES HERE}
    \label{fig:FIGURE NAME GOES HERE}

\end{figure}
\end{document}

(Using How to draw a irregular circle(shape)?, and this, I am trying to make phase diagrams instead of drawing them by hand.)

Answer 1

Here is another fractal solution using Tikz (and not pgf).

I define a new to path style named fractal line with two parameters:

1. the ratio of length to move the middle of each segment.

2. the minimum length to apply the recurrence.

Example of usage to draw an fractal line between (0,0) and (5,0):

\draw (0,0) to[fractal line=.1 and 1mm] (5,0);

The complete code:

\documentclass[convert={size=480},margin=1mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\tikzset{
  fractal line/.style args={#1 and #2}{%
    % #1 is ratio of length to move the middle of each segment
    % #2 is the minimum length to apply the recurrence
    to path={
      let
      \p1=(\tikztostart), % start point
      \p2=(\tikztotarget), % end point
      \n1={veclen(\x1-\x2,\y1-\y2)}, % distance 
      \p3=($(\p1)!.5!(\p2)$), % middle point
      \p4=(rand*#1*\n1,rand*#1*\n1), % random vector
      \p5=(\x3+\x4,\y3+\y4) % random moved middle point
      in \pgfextra{
        \pgfmathtruncatemacro\mytest{(\n1<#2)?1:0}
        \ifnum\mytest=1 %
        \tikzset{fractal line/.style args={#1 and #2}{line to}}
        \fi
      } to[fractal line=#1 and #2] (\p5) to[fractal line=#1 and #2] (\p2)
    },
  },
}

\begin{document}
\begin{tikzpicture}
  \draw[rounded corners=1mm,-stealth] (0,0) to[fractal line=.05 and 1cm] (10,0);
  \draw[rounded corners=.3mm,-stealth] (0,0) to[fractal line=.2 and 3mm] (4,4);
\end{tikzpicture}
\end{document}

Answer 2

In answer to your original question, the following draws a fractal path connecting two points. In this case (0,0) to (3,3)

\documentclass{article}
\usepackage{tikz}

\usetikzlibrary{calc}

% zero mean Gaussian random number with variance=1
\newcount\gaussF
\edef\gaussR{0}
\edef\gaussA{0}

\makeatletter
\pgfmathdeclarefunction{randgauss}{0}{%
 \global\advance\gaussF by\@ne
 \ifodd\gaussF
  \pgfmathrnd@%
  \pgfmathadd@{.0000001}{\pgfmathresult}%
  \pgfmathln@{\pgfmathresult}%
  \pgfmathmultiply@{-2}{\pgfmathresult}%
  \pgfmathsqrt@{\pgfmathresult}%
  \global\let\gaussR=\pgfmathresult%radius = $sqrt(-2*ln(rnd))$
  \pgfmathrnd@%
  \pgfmathmultiply@{360}{\pgfmathresult}%
  \global\let\gaussA=\pgfmathresult%angle = $360*rnd$
  \pgfmathcos@{\pgfmathresult}%
  \pgfmathmultiply@{\pgfmathresult}{\gaussR}%
 \else
  \pgfmathsin@{\gaussA}%
  \pgfmathmultiply@{\gaussR}{\pgfmathresult}%
 \fi
}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcounter{fracI}
\newcount\fracN

\edef\fracF{0.5}% Controls shape of fractal.  Must be < 1.
\edef\fracNPT{64}% number of points to plot

\begin{document}

\begin{center}
\makeatletter
\begin{tikzpicture}
 \pgfmathadd{1}{-\fracF}%
 \global\let\fracS = \pgfmathresult%
 \global\fracN = \fracNPT
 \global\divide\fracN by\tw@
 \coordinate (frac0) at (0,0);% starting point
 \coordinate (frac\fracNPT) at (3,3);% ending point
% calculate perpendicular.  Can replace 1cm with scale factor.
 \coordinate (fracP) at ($(frac0)!1cm!90:(frac\fracNPT) - (frac0)$);

 \global\c@fracI = \z@
 \edef\fracR{frac0}
 \loop\ifnum\fracN > \z@ 
  \ifnum\c@fracI < \fracNPT\relax
   \global\let\fracL = \fracR%
   \global\advance\c@fracI by \fracN
   \edef\fracM{frac\arabic{fracI}}
   \global\advance\c@fracI by \fracN
   \edef\fracR{frac\arabic{fracI}}
   \pgfmathmultiply{\fracS}{randgauss}%
   \global\let\fracY = \pgfmathresult%
   \coordinate (\fracM) at ($(\fracL)!0.5!(\fracR) + \fracY*(fracP)$);
  \else
   \global\divide\fracN by\tw@
   \pgfmathmultiply{\fracS}{\fracF}%
   \global\let\fracS = \pgfmathresult%
   \global\c@fracI = \z@
   \edef\fracR{frac0}
  \fi
 \repeat
% now draw line
 \setcounter{fracI}{0}
 \edef\fracR{frac0}
  \loop\ifnum\c@fracI < \fracNPT\relax
  \stepcounter{fracI}
  \global\let\fracL = \fracR
  \edef\fracR{frac\arabic{fracI}}
  \draw (\fracL) -- (\fracR);
 \repeat
\end{tikzpicture}
\makeatother
\end{center}

\end{document}