Funny pictures of sexps

[bo198214]

The answer can be found by considering the intuitive slog first (because I don't really see how to get to the intuitive slog from the regular slog by reasoning alone, but perhaps you or sheldon can help me here?).

Start with the islog, developed at 0. Create a straight line, from the origin to the upper primary fixed point, and call this line L1. If we calculate the islog of all the points of L1, we will trace out a curve that goes up and slightly to the left, that eventually straightens into a straight line, with slope equal to about -4.2034 for base e. Call this image L2.

....

I dont think one can not understand this without having taken a proper look at the pictures.
Fortunately what you (also previously) describe does not only apply to the intuitive slog but I remember the pictures that Dmitrii made about his Cauchy slog.
(They are scattered over the forum. Particularly this image depicts I think L2, as the left border. It depicts cslog(G) where G is the region bounded by L1 and exp(L1), though L1 extends here also to the lower fixed point. This region is particularly also used by Kneser in his construction which though is not of computational nature.)

So remembering these pictures I can follow you at least a bit.
If I believe what you write I am asking myself where the specific *intuitive* slog is relevant. I guess you could do that construction with every slog and always get as a limit the regular slog. Because you would continue every slog that is defined on G to the whole plane except to the primary fixed points and cuts and somehow it seems as these coarse properties suffice for your construction instead of it relying on the fine grained structure directly on G.

But I admit I am not so deep into that construction (particularly I didnt optically verify your described resemblence to the rsexp) so you tell me!