ifstype.generations

This module implements the ifstype.generations.Generations class which governs the computation of the transition graph from an IFS and other child dependency relationships.

Public module attributes:

• Generations

• LengthFunction

class ifstype.generations.Generations(ifs: ifstype.ifs.IFS)

Compute children relationships and the transition graph based on a fixed iterated function system.

Initialization:

• __init__()

Methods to compute the transition graph:

• compute_graph()

Methods to determine IFS properties:

• verify_fnc()

Methods to compute children:

• child_intervals()

• children()

• children_with_transition()

compute_graph(depth: int = 2000, root: Optional[ifstype.ifs.NetInterval] = None, non_red_nbs: Optional[set] = None) → ifstype.graph.TransitionGraph

Compute the transition graph based on the stored IFS.

This method will compute the children for at minimum depth net intervals before stopping; if this method does not terminate earlier, the transition graph may be incomplete.

To verify completeness of thetransition graph, see ifstype.Graph.is_fnc

See also verify_fnc().

Parameters

• depth – the minimum number of net intervals for which children have been computed before stopping.

• root – the root net interval from which the transition graph should be computed.

• non_red_nbs – a (previously computed) set of reduced neighbours from which the neighbours most be drawn

Returns

the transition graph

verify_fnc(depth: int = 2000) → Tuple[bool, int]

Attempt to verify if the stored IFS satisfies the finite neighbour condition.

This method is a pared down version of compute_graph(), where only the graph dependency structure is computed (without creating the transition graph). The method will compute the children for at minimum depth distinct neighbour sets. It returns a verification pair (bool, computed).

See also compute_graph().

• If bool is true, then the IFS satisfies the finite neighbour condition with at most computed distinct neighbour sets (there may be fewer).

• If bool is false, then the IFS may or may not be weak finite type, but there are at least computed distinct neighbour sets.

Parameters

depth – the minimum number of net intervals for which children have been computed before stopping.

Returns

the verification pair

children(nb_set: ifstype.ifs.NeighbourSet) → Sequence[ifstype.ifs.NeighbourSet]

Construct the neighbour sets which are the children of a net interval.

See also children_with_transition().

Parameters

nb_set – the neighbour set to compute the children of

Returns

sequence of neighbour sets

children_with_transition(nb_set: ifstype.ifs.NeighbourSet, non_red_nbs=None, length_func=<function LengthFunction.transition>) → Sequence[Tuple[ifstype.ifs.NeighbourSet, ifstype.graph.EdgeInfo]]

Compute the transition tuple for every child of the given neighbour set.

This creates a sequence of ifstype.graph.EdgeInfo, one for each child of the neighbour set. These quantities are invariant of the specific net interval which has given neighbour set and are used as edge attributes of the transition graph. See compute_graph() for a usage case, and children() for an analgous method without computing the edge info

Parameters

• nb_set – the neighbour set for which to compute transition tuples

• length_func – the length function used to assign a length to each edge

Returns

ordered sequence of pairs of the child neighbour set and the edge info, one for each child

__init__(ifs: ifstype.ifs.IFS) → None

Initialize the Generations object.

Parameters

ifs – the iterated function system

child_intervals(new_nbs: Iterable[ifstype.ifs.Neighbour]) → Sequence[ifstype.exact.interval.Interval]

Compute all possible normalized intervals formed by endpoints below a net interval [0,1] with from an iterable of neighbours new_nbs.

Parameters

new_nbs – an iterable of neighbours

Returns

a list of intervals in ascending order