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An example from the book "Chaos and Fractals
New Frontiers of Science" shows how unreliable
can be calculations with finite accuracy.
Two different implementations
of the same quadratic law used:
p=p+r*p*(1-p) and
p=(1+r)*p-r*p^2, which is mathematically the same,
but results are far from that.
This simple SDL code is to demonstrate this feature:
//--------------------------8<---------------------
camera {
location <0,0.5,-1> look_at 0
}
background{rgb 1}
#local p0=0.01;
#local p1=p0;
#local p2=p0;
#local r=3;
#local d=0.01;
#local i=0;
#declare Object=union{
#while (abs(p1-p2)<1.3)
#local p1 = p1+r*p1*(1-p1);
#local p2 = (1+r)*p2-r*p2*p2;
sphere{<i/100,p1-p2,0>, d}
#local i=i+1;
#end
}
#debug concat(str(i,1,0),"\n")
#declare Object=#object{Object
#local vv=-(max_extent(Object)-min_extent(Object))/2;
translate vv-min_extent(Object)
scale 0.5/vlength(vv)
}
#object{Object}
//--------------------------8<---------------------
Calculations start with both p1 and p2 = 0.01,
and (under Win32) stop at step 187 when the difference
between them(expected to be always 0) is more then 1.3!
What do you think about it?
Gleb
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In article <3cda84cd@news.povray.org> , "Gleb" <gk1### [at] soton acuk> wrote:
> Calculations start with both p1 and p2 = 0.01,
> and (under Win32) stop at step 187 when the difference
> between them(expected to be always 0) is more then 1.3!
> What do you think about it?
Are you surprised about this when using floating-point numbers?
Thorsten
____________________________________________________
Thorsten Froehlich, Duisburg, Germany
e-mail: tho### [at] trfde
Visit POV-Ray on the web: http://mac.povray.org
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