Strange Nest behaviour with functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg114099] Strange Nest behaviour with functions*From*: István Zachar <zac at freemail.hu>*Date*: Tue, 23 Nov 2010 06:01:36 -0500 (EST)

Dear Group, could someone please explain why Nest yields different results for pure and non pure functions for certain parameter values? The first example (with r = 3.5) produces the same lists, while the second (with r = 3.6) fails to do that. Should pure and non-pure functions differ in this aspect? For larger values of r, the divergence is even more pronounced. In[60]:= func[r_,x_]:=r x (1-x); r=3.5; d1=Nest[r # (1-#)&,Range[0,1,0.2],100] d2=Nest[func[r,#]&,Range[0,1,0.2],100] d1==d2 Out[62]= {0.,0.826941,0.38282,0.38282,0.826941,0.} Out[63]= {0.,0.826941,0.38282,0.38282,0.826941,0.} Out[64]= True In[65]:= r=3.6; d1=Nest[r # (1-#)&,Range[0,1,0.2],100] d2=Nest[func[r,#]&,Range[0,1,0.2],100] d1==d2 Out[66]= {0.,0.899672,0.456407,0.456408,0.899672,0.} Out[67]= {0.,0.899672,0.456409,0.456409,0.899672,0.} Out[68]= False