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Unformatted text preview: es of (a) has the same orientation as (a), so some reﬂections or rotations are involved. For piece A, rotation by π achieves the right
orientation, but places that copy in quadrant III. In order to place the rotated
copy in the right position, translate by e = f = 1/2. The orientation of B is
obtained be reﬂecting across the y -axis, or by a rotation of π/2. This places the
copy in quadrant II, so e = 1 is needed to position the piece correctly. For C ,
reﬂect across the x-axis or rotate by −π/2, and translate by f = 1. This fractal
is produced by IFS 1 and of course by several others. Note that the orientation
of (a) also can be achieved by a rotation through π/2 and a reﬂection.
None of the three pieces of (b) has the same orientation as (b). Part A is reﬂected across the y -axis, then rotated by π/2, placing it in quadrant III, so
e = f = 1/2 places this copy in the right location. Rotating and reﬂecting a paper copy of the shape may help develop visual intuition about these opera...
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