A period-N sequence. Honest-Rejection foil for the monotone / Cauchy rows (a non-constant periodic sequence is bounded but neither monotone nor Cauchy). More...

Concept definition

template<typename Seq, std::size_t N>
concept dedekind::sequences::IsPeriodicSequence = 
    (N > 0) && IsSequence<Seq> && is_periodic_sequence_v<Seq, N>

Detailed Description

A period-N sequence. Honest-Rejection foil for the monotone / Cauchy rows (a non-constant periodic sequence is bounded but neither monotone nor Cauchy).

Requires N > 0: "period 0" is undefined (the s(n) = s(n+N) reading degenerates), so the concept rejects N == 0 regardless of any accidental trait opt-in.

Mandelbrot connection

In :numbers::mandelbrot, a parameter c in a hyperbolic component of period N has an orbit that settles into an attracting N-cycle — eventually period-N. The main cardioid is the period-1 component (the orbit converges to an attracting fixed point — eventually IsAbsorptiveSequence); the period-2 bulb is eventually period-2; and so on. The bulbs of the Mandelbrot set are the geometric picture of IsPeriodicSequence on the z↦z²+c iteration.