4 ms·

All of these are aperiodic; it says as much in the first paragraph. Are you talking about the rotational symmetry?

• abetusk 3y ago
  Yes, the high level rotational symmetry. There's some gross level structure that's preserved while the individual points are (presumably) completely aperiodic/chaotic. What's some insight into the gross level symmetric features appearing? How do you convert something that's completely periodic to an aperiodic/chaotic system with gross level periodic structure? What are the operations that allow the gross level periodic structure to remain while making the fine grained structure aperiodic/chaotic?
  • alimw 3y ago
    They iterate f where f(z) = (a₀ + a₁ z ź + a₂ Re(zⁿ) + a₃ i) z + a₄ źⁿ⁻¹. You can easily check that f(z exp(i 2 π / n)) = exp(i 2 π / n) f(z).
    • abetusk 3y ago
      Thank you!