In[16]:= T@8w_, x_, y_, z_<D = Module@8ww, xx, yy, zz<, ww = Hx + zL ê w; xx = ww y ê x;yy = Hxx zL ê HHxx + zL yL; zz = ww yy ê z; Return@FullSimplify@8ww, xx, yy, zz<DDD

Out[16]= ReturnB:x + z

w,y Hx + zL

w x,

z Hx + zL

x Hw z + yL + y z,

Hx + zL2

w Hx Hw z + yL + y zL>F

In[43]:= M = Table@0, 810 000<D;

In[44]:= M@@1DD = 81.0, 2.0, 3.0, 4.0<

Out[44]= 81., 2., 3., 4.<

In[45]:= For@n = 2, n § 10 000, n++, M@@nDD = T@M@@n - 1DDDD

In[46]:= ListPlot@M@@All, 1 ;; 2DDD

Out[46]=

1 2 3 4 5 6

2

4

6

8

10

12

In[48]:= ListPlot@M@@All, 2 ;; 3DDD

Out[48]=

2 4 6 8 10 12

1

2

3

4

In[49]:= ListPlot@M@@All, 3 ;; 4DDD

Out[49]=

1 2 3 4

2

4

6

8

10

12

2 Untitled-1