Note that applying all three of these transformations to the gasket gives the gasket again. | ||
Click the gasket picture to see the effect of applying these transformations to the gasket. | ||
That is, the gasket is invariant under the simultaneous application of these three transformations. | ||
In fact, the gasket is the only (compact) shape left invariant. | ||
  What happens if we apply these transformations to some shape other than the gasket? | ||
  What happens if we apply these transformations to the resulting shape? | ||
  What happens if we iterate this process? Click the drawing for an animation, or try your own drawing in the deterministic IFS software. | ||
On the left is an instance of this idea applied to a sketch of my cat, on the right to a sketch of my brother. Click each picture to see the process applied. Click the last picture in the sequence to return to the first. | ||
We observe a sequence of pictures that converges to the gasket, independently of the starting shape. With a scanner and imagination, some mischief can be achieved. |
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