Hacker News Reader

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

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?

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).

Thank you!

Reply on news.ycombinator.com