What is the default tick mark function for FrameTicks?

Question

According to the documentation of Ticks, a ticks function

The tick mark function func[Subscript[x, min],Subscript[x, max]] may return any other tick mark option

For example,

tickFunc = Subdivide[#1, #2, 6] &;
Plot[x, {x, -0.1, 3}, Frame -> True, 
 FrameTicks -> {{Automatic, Automatic}, {tickFunc, Automatic}}]

Will show

But I want to know what is the default tick mark function when setting Ticks to Automatics?

A simple manipulate like

Manipulate[Plot[x, {x, -0.1, n}, Frame -> True], {n, 1, 200, 1}]

does show some definite feature of ticks, for example, number of ticks is always between 4 and 8. But I failed to construct a tick mark function behave as default. Does anyone have ideas?

Answer 1

You can get a fairly close approximation using the internal functions Charting`ScaledTicks and Charting`ScaledFrameTicks:

GraphicsRow[{
    Graphics[
        {}, PlotRange->{{0,1},{1,10}},Frame->True,AspectRatio->1
    ],
    Graphics[
        {}, PlotRange->{{0,1},{1,10}},Frame->True,AspectRatio->1,
        FrameTicks->{
            {
                Charting`ScaledTicks[{Identity,Identity}],
                Charting`ScaledFrameTicks[{Identity,Identity}]
            },
            {
                Charting`ScaledTicks[{Identity,Identity}],
                Charting`ScaledFrameTicks[{Identity,Identity}]
            }
        }
    ]
}]

You'll notice that the origins are different.

If you look at the output of plotting functions, you will sometimes see these internal functions:

Options[LogPlot[x, {x, 1, 10}], Ticks]

{Ticks -> {Automatic, Charting`ScaledTicks[{Log, Exp}]}}