Question: procedure inside for loop

Now I have written this for loop just intuitively but unfortunately it doesnt work:

x(0):=0.5

for N from 1 to 100 do

x:=proc(n) option remember; eval(r*x(n-1)*(1-x(n-1)),r=4/(100)*N) end proc;

l(N):=[seq(x(n),n=20..100)]

end:

What's the specific problem maple has?

 

Edit: problem solved: 

for N from 1 to 100 do

x:=proc(n) option remember; eval(r*x(n-1)*(1-x(n-1)),r=4/(100)*N) end proc;

x(0):=0.5

l(N):=[seq(x(n),n=20..100)]

end:

 

whatever the reason the assignment of x(0) has to be after the procedure has been defined

 

But I'm wondering why each l(N) is the same.

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