Petite illusion d'optique

Les lignes horizontales dans la figure ci-dessous sont-elles parallèles? En cliquant sur le bouton en bas à gauche vous pourrez observer le glissement d'une ligne sur deux et ainsi apprécier l'illusion…

carre.mp
%@AUTEUR: Maxime Chupin
%@DATE: 3 mars 2007

verbatimtex
%&latex
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage[mdugm]{mathdesign}
\begin{document}
etex

u = 1cm;
path carre,droite;
carre := (1,1)--(-1,1)--(-1,-1)--(1,-1)--cycle;
droite := (-20u,0)--(20u,0);
numeric max;
max := 9;

for i:=0 upto 20:
beginfig(i+1);

for y:=0 upto max :
draw droite shifted (10u,y*u) withpen pencircle scaled 1;
endfor;

for w:=0 upto 4:
for x:=0 upto max:
fill carre scaled (0.5*u) shifted (0.5u+2*x*u,0.5*u+2w*u);
endfor;
endfor;

for w:=0 upto 3:
for x:=(-1) upto (max+1):
fill carre scaled (0.5*u) shifted ((0.5+i/20)*u+2*x*u,0.5*u+2w*u+u);
endfor;
endfor;

label.urt(btex \begin{LARGE}Petite illusion d'optique\end{LARGE} etex,
(7.5u,-u));

clip currentpicture to
(-0.5u,-u)--(20u,-u)--(20u,max*u)--(-0.5u,max*u)--cycle;

endfig;
endfor;

for i:=0 upto 40:
beginfig(22+i);

for y:=0 upto 8 :
draw droite shifted (10u,y*u) withpen pencircle scaled 1;
endfor;

for w:=0 upto 4:
for x:=0 upto 9:
fill carre scaled (0.5*u) shifted (0.5u+2*x*u,0.5*u+2w*u);
endfor;
endfor;

for w:=0 upto 3:
for x:=(-1) upto (max+1):
fill carre scaled (0.5*u) shifted ((1.5-i/20)*u+2*x*u,0.5*u+2w*u+u);
endfor;
endfor;

label.urt(btex \begin{LARGE}Petite illusion d'optique\end{LARGE} etex, (7.5u,-u));

clip currentpicture to
(-0.5u,-u)--(20u,-u)--(20u,max*u)--(-0.5u,max*u)--cycle;

endfig;
endfor;

for i:=0 upto 20:
beginfig(63+i);

for y:=0 upto 8 :
draw droite shifted (10u,y*u) withpen pencircle scaled 1;
endfor;

for w:=0 upto 4:
for x:=0 upto 9:
fill carre scaled (0.5*u) shifted (0.5u+2*x*u,0.5*u+2w*u);
endfor;
endfor;

for w:=0 upto 3:
for x:=(-1) upto (max+1):
fill carre scaled (0.5*u) shifted ((-0.5+i/20)*u+2*x*u,0.5*u+2w*u+u);
endfor;
endfor;

label.urt(btex \begin{LARGE}Petite illusion d'optique\end{LARGE} etex, (7.5u,-u));

clip currentpicture to
(-0.5u,-u)--(20u,-u)--(20u,max*u)--(-0.5u,max*u)--cycle;

endfig;
endfor;

end