MapConrec6demo

MapConrec6demo is technical aeticle; it is collection of pictures created as demonstration of use of routine Conrec6.cin.

That routine is designed by ChatGPT and Dmitrii Kousnetsov (2025) for generation of Complex maps.

Routine Conrec6.cin is created as modern substitute of the earlier and "dirty" routine conto.cin from Citizendium .

The contouring subroutine "Conrec" is used as a prototype for the new version Conrec6.cin.

The compilation of C++ file with that routine requires options "-std=c++11 -O2"

The routine Conrec6.cin is still under testing.

However, you may use it for your own risk.

Attribute the source; indicate your modifications, if any. This helps to trace errors, if any.

The generators are supplied in descriptions of the pictures (click on the picture).

The first four functions shown below are trivial elementary functions.

Pics

Maps of the following functions are shown below: \(z\!\mapsto\! z\) (Identity function), \(z\!\mapsto\! z^2\), \(z\!\mapsto\! \log(z)\), \(z\!\mapsto\! \sqrt{z}\), \(z\!\mapsto\! \)Filog\((z)\).

in each case, function \(z\!\mapsto\! f(z)\) is shown with lines of constant its real part and lines of constant its imaginary part: \[ u + \mathrm i v = f(x\!+\!\mathrm i y) \]

Lines \(u = \mathrm{const} \) and lines
Lines \(v = \mathrm{const} \) are drawn.

Integer values of \(u\) and \(v\) are drawn with thick lines.
The thin lines are drawn with step 1/10.

Integer values of \(u\) are shown with black thick lines.

Positive integer values of \(v\) are shown with blue thick lines. Negative integer values of \(v\) are shown with red thick lines. Isoline \(v\!=\!0\) is shown with dark pink thick line.

Other (non-integer) values of \(v\) are shown with dark green thin lines.

Non-integer positive values of \(u\) are shown with thin blue lines.

Non-integer negative values of \(u\) are shown with thin red lines.

This style is used in the majority of complex maps loaded at TORI and, in particular for those that are used in book Superfunctions.

In the first four pictures, in order to keep them simple, the labels are not added. The grid lines are drown from -3 to 3 with step unity (not to be confused with step of the mesh) both alone the real axis and along the imaginary axis.

The in the fifth picture, the grid lines are drawn with step 0.1; the labels are added. The map reproduces the bottom part of Fig.18.2 at page 248 of book «Superfunctions», 2020.
The original is generated with historic routine conto.cin ; it is shown as the 6th picture.
The 5th and 6th pictures use the same set of labels; and the contour lines look identical; it is very difficult to see any difference between these two pictures; they look the same.

Warnings

Routine Conrec6 is still under testing.

You may get the preliminary version from the description of any of pictures above or from article Conrec6.cin and use at your own risk.

Attribute the source and the modification(s) if any.
This helps to trace errors, if any.

The numbering of versions of the routine in TORI is not yet established.
The “6” in name "Conrec6.cin" refers to the 6-digit precision used for EPS output coordinates, not to version numbering.
Even ChatGPT got confused with this "6". Sorry about the naming.
If you make a new version of the routine to plot complex maps, better than "conto.cin" and better than "Conrec6.cin", choose a better name for it.

References

Keywords

«Ado.cin», «ChatGPT», «Complex map», «Conrec6.cin», «conto.cin», «Filog.cin», «MapConrec6demo», «LogTestMaps»,