\documentclass{standalone} 
\usepackage{tikz} %%Generate vector graphics from within LaTeX
\usepackage{ifthen}
\usetikzlibrary{patterns,decorations}

\newcommand*{\scale}{0.5}  
\newcommand*{\gridlinewidth}{thin}  
\newcommand*{\pathlinewidth}{1.5}  
    
\begin{document}                    
	\begin{tikzpicture}[>=stealth]
		
		%\draw[step=.5cm,gray,\gridlinewidth] (0,-2.4) grid (13.4,1.4);
		
		%otherwise y-axis is cropped to the left
		\draw [white] (-0.06,0);
		
		%otherwise pic jumps
		\draw [white] (1.5*\scale,-3.2*\scale);
		\draw [white] (1.5*\scale,3.2*\scale);
		
		%axes
		\draw[->] (0,0) -- (0,1.5) {};
		\draw[->] (0,0) -- (15.5,0) {};		
		
		
		%walk
		\def\mywalk{%
		1/1,2/2,3/3,4/0,5/1,6/2,7/3,
		8/4,9/5,10/0,11/0,12/1,13/2,14/3,15/4,16/0,17/1,18/2,
		19/3,20/4,21/0,22/1,23/0,24/1,25/2,
		26/3,27/4,28/5,
		29/0,30/1}
		\draw[-, line width=\pathlinewidth] (0,0)
		\foreach \x/\y in \mywalk
		{	-- (\scale*\x,\scale*\y) };
		
		
			
		\foreach \x/\y in \mywalk
		{	
			\fill (\x*\scale,\y*\scale) circle (2pt)
				%\ifnum \y<0 node [anchor=south] {\large -}
				%\else\ifnum \y>0 node [anchor=north] {\large +}
				%\else node [anchor=north] {0} \fi\fi
				;
			}		
		 \fill (0,0) circle (2pt) node[anchor=north] {};
		
		\foreach \x/\y in \mywalk
		{
			\ifthenelse{\y=5}{
				\fill[color=red] (\x*\scale,\y*\scale) circle (3pt);
			}{}
\ifthenelse{\y=0}{
				\fill[color=blue] (\x*\scale,\y*\scale) circle (3pt);
			}{}
		}
		
	\end{tikzpicture}
\end{document}