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Friday, 23 May 2008 02:14
Iterations of real function x_n+1 = f( x_n ) = x_n² + c We begin with this demonstration, where map f^oN(x) = f(f(...f(x))) is the blue curve, y = x is the green line and -2 < x,y < 2. C coincides with the Y one because y(0) = f(0) = C. Dependence x_n on n is ploted in the right window. Read more Add comment (0) Hits: 131

Friday, 23 May 2008 02:10
For the Third level bulbs we have ( ^m₁ / n₁ ^m₂ / n₂ ^m₃ / n₂ ) index. Here you can see ( ¹/₃ ¹/₄ ¹/₅ ) bulb. It has three different regions in his "antenna" with 3, 4 and 5 spokes (in the square region) Read more Add comment (0) Hits: 209

Friday, 23 May 2008 02:07
Every ( ^m₁ / n₁ ) primary bulb has decoration very similar to the main bulb one (in "square" parametrisation). So for the secondary bulbs we have simply to add one more ^m₂ / n₂ rotation number ( ^m₁ / n₁ ^m₂ / n₂ ). Note that period of a secondary bulb is n₁ x n₂ product. In this way we can map all the M-set decorations. Read more Add comment (0) Hits: 158