Deprecate {ContourSet,Quiver}.ax in favor of .axes. - #16058

The use of attributes .ax vs .axes is a mess. Instead of fixing single issues like here or in ContourSets in #12443, we need to

1. Evaluate the current state
2. Decide which one is the preferred solution.
3. Consistently change it everywhere in the code base.

Step 1: Current state

Usages of self.ax (searched for self.ax = ):

• Quiver
• ColorbarBase
• ContourSet
• Sankey
• AxesWidget
• ToolHandles
• axes_grid1.ColorbarBase

Usages of self.axes (searched for self.axes = ):

• AxisArtist
• Artist
• _AxesBase (which is an Artist)
• axis_grid1.Axes
• Tick
• Axis
• _ImageBase
• Legend
• VertexSelector
• _ThetaShift
• Spine
• MultiCursor
• GridHelperRectlinear

Step 2: Preferred solution

Pro self.ax:

• The canonical variable name is ax (fig, ax = plt.subplots()).
  • It's easy to guess/remember if you are familiar with matplotlib conventions.
  • That choice was deliberate to prevent plural naming issues when collections containing Axes.

Pro 'self.axes`:

• More classes currently use this variant. But I'm not clear for which classes this attribute is accessed by users; so not sure deprecating ax would have the smaller impact on users.
• The name is more readable for the uninformed user (but then again does he know what an axes is?).

IMHO, there's no clear winner. I slightly lean towards keeping self.ax. But this is really up for discussion.

More classes currently use this variant.

Just to be clear, it's a lot more classes, in practice (not just 13 vs 7 like the count above suggests): all Artists have .axes, so that's also Line2D, all the Collections, all the Patches, etc... which are also much more commonly used than any of the classes that use .ax. And as a consequence, other classes (e.g. Colorbar, as noted in #15986 (comment), but also Animation) also typically assume that they can access parent axes of other objects (which are typically artists, but not always) with .axes.

As the most likely guilty party in establishing the ax attributes, I'm OK with switching to axes. It will be interesting to see how much external code this ends up affecting.

rebased

As we don't have a good sense of how big of an impact this actually has I am in favor of merging this and seeing what push back we get in the rc / 3.3.0. We should definitly have the .axes alias to make the API more uniform and it would be better to have only one way to do this, but if we get too many complaints we should be ready to leave .ax permanently.