dedekind::sequences::OrbitSequence< T, Op > Struct Template Reference

The orbit sequence n ↦ Opⁿ(generator) of a carrier (T, Op), reified as a distinct IsSequence type. More...

Inheritance diagram for dedekind::sequences::OrbitSequence< T, Op >:

Collaboration diagram for dedekind::sequences::OrbitSequence< T, Op >:

Public Member Functions
constexpr	OrbitSequence (T gen, Op op)
Public Member Functions inherited from dedekind::sequences::Path< T, Cardinality, Index >
constexpr Codomain	operator() (Index i) const
constexpr T	at (Index i) const
constexpr std::size_t	size () const noexcept
constexpr auto	begin () const noexcept
constexpr auto	end () const noexcept
constexpr auto	cardinality () const noexcept
	The Path is generally viewed as a mapping from N.

Additional Inherited Members
Public Types inherited from dedekind::sequences::Path< T, Cardinality, Index >
using	Domain = Index
using	Codomain = T
using	cardinality_type = Cardinality
using	index_type = Index
Public Attributes inherited from dedekind::sequences::Path< T, Cardinality, Index >
std::function< T(Index)>	generator
	The underlying mapping f(n).
std::size_t	extent = 0

Detailed Description

template<typename T, typename Op>
struct dedekind::sequences::OrbitSequence< T, Op >

The orbit sequence n ↦ Opⁿ(generator) of a carrier (T, Op), reified as a distinct IsSequence type.

Derives the sequence shape from Path<T>; the generator function folds Op over copies of the stored generator element. The carrier's periodicity (if any) propagates to this type's is_periodic_sequence_v via the bridge below.

Note

When cyclic_order_v<T, Op> = order > 0, the index n is reduced mod order before folding, so at(n) is O(order) rather than O(n) — the orbit only has order distinct values regardless of n.

Group orbit vs.\ iteration

OrbitSequence is the group-flavoured orbit (n ↦ Opⁿ(generator), folding a binary Op). Its dynamical-systems sibling is the unary-iteration sequence n ↦ fⁿ(seed) produced by iterate(seed, f) — e.g.\ mandelbrot_orbit(c) = iterate(0, z↦z²+c) in :numbers::mandelbrot. Both are "iteration sequences"; the sequence-shape concepts (IsBoundedSequence, IsPeriodicSequence, IsAbsorptiveSequence) apply to either regardless of how the orbit is constructed. A future mechanical unification — a typed IterationSequence<f, seed> subsuming both — would let the periodicity bridge fire on Mandelbrot bulbs too; this slice keeps the group-orbit case (where cyclic_order_v gives the period); the unary case for the one step that matters most, the NNO successor, is SuccessorOrbit below.

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The documentation for this struct was generated from the following file:

• src/main/modules/dedekind/sequences/convergence.cppm