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% TeX Mandelbrot Program
%
% My entry for the contest ``The most useless TeX program ever written''.
% Can anyone top that? (Don't mention MusicTeX in this context. That's not
% meant to be a joke.)
% Also welcome: Improvements of this saving on TeX's resources. This takes
% more than five minutes on my NeXT 486/66.
%
% Seb, 6.7.94
%
% (seb@balu.afp.ruhr-uni-bochum.de)
%
%
% parameters that you can modify:
%
% \x, \y, \xmax, \ymax in units of 10000
\newcount\x
\x=-20000 % means -2.000 for real part of start value
\newcount\y
\y=-20000 % imaginary part
\newcount\xmax
\xmax=20000 % end value, real
\newcount\ymax
\ymax=20000 % end value, imaginary
%
% calculation depth
\newcount\mandeldepth
\mandeldepth=100
%
%
% recursation depth = number of pixels.
\newcount\xsize % (Don't go wild, tail recursion
\xsize=100 % uses loads of TeX memory!)
\newcount\ysize
\ysize=100
%
% picture size
\newdimen\height
\newdimen\width
\height=10cm
\width=10cm
%
% that was all the parameters!
%
%
% pixel size:
\newdimen\xgrid
\xgrid=\height
\divide\xgrid by\xsize
\newdimen\ygrid
\ygrid=\width
\divide\ygrid by\ysize
%
\nopagenumbers
%
\newcount\stepX % work out step sizes
\stepX=\xmax
\advance\stepX by -\x
\divide\stepX by\xsize
\newcount\stepY
\stepY=\ymax
\advance\stepY by -\y
\divide\stepY by\ysize
%
\def\cout#1{\immediate\write16{#1}} % type out debug message
%
\def\yes{Y} % some stupid logical macros
\def\no{N}
\def\notyet{x}
%
\newcount\u % variables for calculation
\newcount\v
\newcount\newV
\newcount\newU
\newcount\d
\newcount\h
\def\runmandel{% % recursive Mandelbrot macro
\newU=\u%
\multiply\newU by \u% % newU := u^2
\h=\v%
\multiply\h by \v% % h := v^2
\advance\newU by -\h% % newU := u^2 - v^2
\h=\x%
\multiply\h by 10000% % h := x * 10000 (normalize)
\advance\newU by \h% % newU := newU + h
\divide\newU by 10000% % renormalize u
\newV=\u%
\multiply\newV by \v%
\multiply\newV by 2% % newV := 2 *u * v
\h=\y%
\multiply\h by 10000% % h := y * 10000
\advance\newV by \h% % newV := newV + h
\divide\newV by 10000% % renormalize v
\u=\newU% % newU = u^2 - v^2 + x
\v=\newV% % newV = 2 * u * v + y
\advance\d by 1%
% \cout{d: \the\d, u: \the\u, v: \the\v}%
\ifnum\d>\mandeldepth% % member ofthe Mandelbrot set
\def\result{\yes}%
\fi%
\ifnum\u<-20000%
\def\result{\no}% % real part exceeded -2
\fi%
\ifnum\u>20000%
\def\result{\no}% % real part exceeded 2
\fi%
\ifnum\v<-20000%
\def\result{\no}% % imaginary part exceeded -2
\fi%
\ifnum\v>20000%
\def\result{\no}% % real part exceeded 2
\fi%
\if\notyet\result\runmandel\fi% % play it again...
}%
\def\result{\yes}%
\def\makeline{\advance\x by \stepX%
%\cout{testing \the\x = i * \the\y}%
\u=0%
\v=0%
\d=0%
\def\result{\notyet}%
\runmandel% result expands to either yes or no now
\if\result\yes%
\vrule height \xgrid depth 0pt width \ygrid%
\else%
\vrule height \xgrid depth 0pt width 0pt\hskip\xgrid%
\fi%
\ifnum\x<\xmax%
\makeline%
\else\fi}%
\def\makepicture{\advance\y by \stepY%
\hbox{\makeline}%
%\cout{y in makepicture: \the\y}%
\ifnum\y<\ymax%
\makepicture%
\else\fi}%
\vbox{\offinterlineskip\makepicture} % now, let's go tail
\bye % recursive!
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