We will find the IFS rules for this fractal.
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The original fractal on the left with its decomposition into three copies on the right.
A quick glance shows that there are only three transformations in this example also.
Note the top and bottom left pieces have the same orientation as the entire fractal, while the bottom right piece is rotated.
Keeping in mind that our transformation rules allow only rotations fixing the origin, some care must be taken with the translation after the rotation.
All copies have been scaled by 1/2.
The copy in the T1 position has only been scaled.
The copy in the T3 position has been scaled and translated
vertically by
The copy in the T2 position has been scaled, rotated 90 degrees counterclockwise and translated.
After rotating, the scaled copy will be on the left side of the y-axis. To get it in the correct final position, it must be translated to the right by 1.
| r | s | theta | e | f | |
| T1 | .5 | .5 | 0 | 0 | 0 |
| T2 | .5 | .5 | 90 | 1 | 0 |
| T3 | .5 | .5 | 0 | 0 | .5 |
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