Cyclic Driven IFS

3-Cycle Coordinates

Solving the fixed point equations gives the coordinates of each point. For example,

(x, y) = T3T2T1(x, y) = T3T2(x/2, y/2)

= T3(x/4 + 1/2, y/4) = (x/8 + 1/4, y/8 + 1/2)

so

x = x/8 + 1/4 and y = y/8 + 1/2

Solving for x and y gives (x, y) = (2/7, 4/7).

Similar calculations show

(1/7, 2/7) is the fixed point of T₁T₃T₂

and

(4/7, 1/7) is the fixed point of T₂T₁T₃

Return to 3-Cycles.