25-Intervalos: Conjunto de Cantor
Os primeiros passos no processo iterativo de criar o Conjunto de Cantor .
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restart: with(plottools): with(plots):
intfin1 := proc( a, b )
# description "plot a finite interval on a number line";
local r, M, v1, v2, wid, bar, Axesplot, leftpt, rightpt, pt_color,
leftend, rightend, LT, RT, textpos;
r := b-a ;
M := evalf( 1.2 * (b-a) );
v1 := [a, 0];
v2 := [b, 0];
wid := .1 ;
bar := arrow( v1, v2,
shape = double_arrow, color = green , difference = true,
width = wid, head_width = 0, head_length = 0):
textpos := wid ;
LT := textplot( [a, textpos, a] ):
RT := textplot( [b, textpos, b] ):
if (M > .08)
then display( bar, LT, RT );
else display( bar);
fi;
end proc:
cantorint := proc( a, b, n )
# plot the nth step in Cantor set";
local left, right, len, A, Axisplot;
global count, finished;
finished := false;
left := a; right := b; len := (b-a)/3;
if(n = 1)
then count :=count + 1;
A||count := intfin1( a, b):
print( a, b);
finished := true;
else
cantorint( a, a + len, n-1);
cantorint( b - len, b, n-1);
fi;
if( finished)
then
Axisplot := plot( 0, x = a..b , scaling = constrained,
axes = none, thickness = 2, color = black,
tickmarks = [1,1] ):
display( {Axisplot, seq( A||i, i = 1..(2^(n-1) ))} );
fi;
end proc:
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count := 0:
cantorint( 0, 1, 1);
count := 0:
cantorint( 0, 1, 2);
count := 0:
cantorint( 0, 1, 3);
count := 0:
cantorint( 0, 1, 4);
count := 0:
cantorint( 0, 1, 5);
count := 0:
cantorint( 0, 1, 6);