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\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}
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