Formalize basins with dedicated types

[Datseris]

Describe the feature you'd like to have

At the moment we handle basins of attraction as a standard Julia Array. The grid corresponding to the basins is a separate variable, and the attractors are as well. This has two major problems:

1. It is tedius as one has to carry around the grid and attractors and basins.
2. It does not play well with an alternative formulation of basins that one gets from basins_fractions: the sampled basins. There the basins are not an Array but rather a vector of points.

I think formalizing this concept is a benefit, and it also allows us to extend it naturally and simply to future research.

If possible, sketch out an implementation strategy

• Define abstarct type BasinsOfAttraction{ID}. Always "contains" attractors. Type parameterization ID is what is the thing stored as an attractor label. For standard basins this is Int.
• Define subtype ArrayBasinsOfAttraction. Contains a grid (instance of Grid subtype), and the basin array.
• Define subtype SampledBasinsOfAttraction. Contains two vectors: sampled_points and points_ids. Initial conditions and their labels.

We can then directly pass the instance of such types into functions like final state sensivitty, or the heatmap_basins_attractors, or in general all plotting functions.

We can then extend ProbabilisticBasinsOfAttraction where ID is not Int but rather Dict{Int, Float}, the probability to go to each attractor.

[Datseris]

This also allows us to define a nice function

map_to_basin(basin::BasinOfAttraction, point)

that given a point it interpolates to which basin it should belong. For array basins this is the standard thing we do in the recurrences algotihm ,where we map the point to the closest grid cell:

n = Attractors.basin_cell_index(point, grid)
return basins[n]

while for sampled basins, it could get the nearest neighbor of the point and return the basin of the nearest neighbor.