Figure 1 description

Four same sized rectangles

• Figure 1a: a rectangle with the left side colored blue and right side colored white with a solid red line (a wall) between the two halves.
• Figure 1b: same as figure 1a except no wall between the two halves.
• Figure 1c: same rectangle but colors now in a gradiant from blue at left end to white at the right end.
• Figure 1d: same rectangle but now a solid light blue

Figure 2 description

A green rectangle titled \(X\) with a line (the trajectory) wandering from a dot on the left labeled \(x\) to an arrow on the right labeled \(\phi_t(x)\).

Figure 3 description

A more complex diagram with elements from figure 1 and figure 2. The green rectangle from figure 2 but with different text and with the rectangle divided into several regions by lines.

• region labelled \(X_{M_1}\) includes the starting dot on the left which is now labeled \(x\)
• region labelled \(X_{M_2}\) does not include the trajectory line and is in the upper left of the rectangle
• region labeled \(X_{M_m}\) includes most of the trajectory line except the starting dot and initial segment from it
• An unlabeled region contains a portion of the trajectory line near its start.

Below the green rectangle are three of the four rectangles (b, c, and d) from figure 1. A red arrow from the figure 1b rectangle (blue on the left, white on the right) goes to the \(X_{M_1}\) region around the starting point of the trajectory line. Another red arrow goes from the figure 1c rectangle (gradiant from blue on left to white on right) to the unlabeled region mentioned above. A final red arrow goes from the figure 1d rectangle (uniform light blue) to the region labeled \(X_{M_m}\).