\documentclass{article}
\usepackage[pdftex,a3paper,margin=1pt,landscape]{geometry}
\usepackage{expl3}

%% draw macros
\newcount\mlength
\mlength0
\newcount\cstate
\newdimen\mandelunit
\mandelunit=0.5pt

\def\wp{%
  \ifnum\cstate=1 \global\advance\mlength1
  \else\ifnum\cstate=-1 \vrule width \mlength\mandelunit height \mandelunit depth 0pt \global\mlength1 \fi\fi
  \global\cstate1}
\def\bp{%
  \ifnum\cstate=-1 \global\advance\mlength1
  \else\ifnum\cstate=1 \hspace*{\mlength\mandelunit}\global\mlength1 \fi\fi
  \global\cstate-1}
\def\r{%
  \ifnum\cstate=1\hspace*{\mlength\mandelunit}\else\vrule width \mlength\mandelunit height \mandelunit depth 0pt \fi
  \global\cstate0 \global\mlength0}

\ExplSyntaxOn
  \int_const:Nn \l_hakviiaiii_maxloop {20}
  \fp_const:Nn \l_hakviiaiii_scale {0.002}
  \int_new:N \l_hakviiaiii_loopismandel
  \fp_new:N \l_hakviiaiii_x
  \fp_new:N \l_hakviiaiii_xx
  \fp_new:N \l_hakviiaiii_y
  \fp_new:N \l_hakviiaiii_yy
  \fp_new:N \l_hakviiaiii_a
  \fp_new:N \l_hakviiaiii_b
  \bool_new:N \l_hakviiaiii_check_mandel
  \cs_new:Npn \hakviiaiii_ismandel:nn #1#2{%
    \int_zero:N \l_hakviiaiii_loopismandel
    \fp_zero:N \l_hakviiaiii_x
    \fp_zero:N \l_hakviiaiii_y
    \fp_set:Nn \l_hakviiaiii_xx {\l_hakviiaiii_x * \l_hakviiaiii_x}%
    \fp_set:Nn \l_hakviiaiii_yy {\l_hakviiaiii_y * \l_hakviiaiii_y}%
    \bool_set_false:N\l_hakviiaiii_check_mandel
    \bool_while_do:nn {%
      \int_compare_p:nNn 
        {\l_hakviiaiii_loopismandel}% 
          < {\l_hakviiaiii_maxloop + 1}%
      && \fp_compare_p:nNn
        {\l_hakviiaiii_xx + \l_hakviiaiii_yy}< {4.0}%
      } {%
      \fp_set:Nn \l_hakviiaiii_y {%
        2.0 * \l_hakviiaiii_x *\l_hakviiaiii_y + #2}%
      \fp_set:Nn \l_hakviiaiii_x {\l_hakviiaiii_xx - \l_hakviiaiii_yy + #1}%
      \fp_set:Nn \l_hakviiaiii_xx {\l_hakviiaiii_x * \l_hakviiaiii_x}%
      \fp_set:Nn \l_hakviiaiii_yy {\l_hakviiaiii_y * \l_hakviiaiii_y}%
      \int_set:Nn \l_hakviiaiii_loopismandel 
        {\l_hakviiaiii_loopismandel + 1}%
      }%
    \bool_set:Nn \l_hakviiaiii_check_mandel
      {\int_compare_p:nNn
        {\l_hakviiaiii_loopismandel} > {\l_hakviiaiii_maxloop}}}
  \cs_new:Nn \hakviiaiii_loopmandel: {%
    \fp_set:Nn \l_hakviiaiii_b {1.0}%
    \fp_while_do:nNnn {\l_hakviiaiii_b} > {-1.0 - \l_hakviiaiii_scale} {%
      \fp_set:Nn \l_hakviiaiii_a {-1.5}%
      \fp_while_do:nNnn{\l_hakviiaiii_a} < {0.5 + \l_hakviiaiii_scale} {%
        \hakviiaiii_ismandel:nn{\l_hakviiaiii_a}{\l_hakviiaiii_b}%
        \bool_if:nTF
          {\l_hakviiaiii_check_mandel}%
          {\bp}{\wp}%
        \fp_set:Nn \l_hakviiaiii_a {\l_hakviiaiii_a + \l_hakviiaiii_scale}%
      } \r\\%
      \fp_set:Nn \l_hakviiaiii_b {\l_hakviiaiii_b - \l_hakviiaiii_scale}% 
    }}
  \cs_new_eq:NN \mandel \hakviiaiii_loopmandel:
\ExplSyntaxOff
\begin{document}
  \thispagestyle{empty}\noindent
  \leavevmode\baselineskip=\mandelunit
  \mandel
\end{document}