Cyclic Driven IFS
3-Cycle Coordinates
Solving the fixed point equations gives the coordinates of each point. For example,
(x, y)
= T
3
T
2
T
1
(x, y) = T
3
T
2
(x/2, y/2)
= T
3
(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 T
1
T
3
T
2
and
(4/7, 1/7)
is the fixed point of T
2
T
1
T
3
Return to
Cyclic IFS
.