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Joseph O'Rourke
Joseph O'Rourke
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An illustration offor @Toscho's nice idea, from Steven Dutch's Rep-Tiles webpage:

  ![reptiles][1]
"Four squares can be arranged around a central square to form a Greek Cross. Greek Crosses make a lovely plane tesselation, but they are not rep-tiles. We can try modifying a Greek Cross tesselation by replacing each cross with the compound of five crosses. It's closer, but still not an exact rep-tile. We can repeat the process, each time getting figures that are more and more crinkled and closer to a true rep-tiling. But at every step, we see that the perimeter of the tiling always has twice as many crinkles as each tile."

An illustration of @Toscho's nice idea, from Steven Dutch's Rep-Tiles webpage:

  ![reptiles][1]
"Four squares can be arranged around a central square to form a Greek Cross. Greek Crosses make a lovely plane tesselation, but they are not rep-tiles. We can try modifying a Greek Cross tesselation by replacing each cross with the compound of five crosses. It's closer, but still not an exact rep-tile. We can repeat the process, each time getting figures that are more and more crinkled and closer to a true rep-tiling. But at every step, we see that the perimeter of the tiling always has twice as many crinkles as each tile."

An illustration for @Toscho's nice idea, from Steven Dutch's Rep-Tiles webpage:

  ![reptiles][1]
"Four squares can be arranged around a central square to form a Greek Cross. Greek Crosses make a lovely plane tesselation, but they are not rep-tiles. We can try modifying a Greek Cross tesselation by replacing each cross with the compound of five crosses. It's closer, but still not an exact rep-tile. We can repeat the process, each time getting figures that are more and more crinkled and closer to a true rep-tiling. But at every step, we see that the perimeter of the tiling always has twice as many crinkles as each tile."
Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 29.9k
  • 6
  • 62
  • 140

An illustration of @Toscho's nice idea, from Steven Dutch's Rep-Tiles webpage:

  ![reptiles][1]
"Four squares can be arranged around a central square to form a Greek Cross. Greek Crosses make a lovely plane tesselation, but they are not rep-tiles. We can try modifying a Greek Cross tesselation by replacing each cross with the compound of five crosses. It's closer, but still not an exact rep-tile. We can repeat the process, each time getting figures that are more and more crinkled and closer to a true rep-tiling. But at every step, we see that the perimeter of the tiling always has twice as many crinkles as each tile."