Some affine maps have certain points that when plugged in, give themselves. Causing an infinite loop. Take FCF for example:
F1F( -1/2x+1/2, 1/2y).......F1F( 1/3, 0) ---> ( 1/3, 0)
F2C( -1/2x+1, -1/2+1/2).....F2C(2/3, 1/3)--->(2/3, 1/3)
F3F( -1/2x+1/2, 1/2y+1/2)...F3F(1/3, 1) --->(1/3, 1)
It is interesting to note that the repeating points in F1 and F3 are the end points of the straight line between the two sections. It is also interesting to note that if you took the point (1/3, 1/4) and put it through F1F it would approach the point (1/3 , 0) since 1/3 would stay 1/3 and 1/4 would become 1/8 which would become 1/16 getting infinitely smaller. These point seem something like the attractors I read about earlier. They help when trying to prove if two sections are connected.
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