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Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Edit: Sorry, I didn't realize you required it to be connected. Solenoids still work, but Antoine's necklace is out.

Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Edit: Sorry, I didn't realize you required it to be connected. Solenoids still work, but Antoine's necklace is out.

Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Edit: Sorry, I didn't realize you required it to be connected. Solenoids still work, but Antoine's necklace is out.

Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Edit: Sorry, I didn't realize you required it to be connected. Solenoids still work, but Antoine's necklace is out.

Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Have you tried solenoids? Solenoids certainly seem like they would satisfy your definition. Also, Antoine's necklace is another likely candidate.

Edit: Sorry, I didn't realize you required it to be connected. Solenoids still work, but Antoine's necklace is out.