ContoTestQuadraticMap

ContoTestQuadraticMap is comparison of complex maps of function \( z \mapsto z^2 \) generated with two divergent routines:

1. Routine conto.cin from Citizendium

2. Routine conto01.cin written by ChatGPT 2025.08.29; it is preliminary version, it is not optimized.

The maps are shown below.

Function \(f=z^2 \) is plotted in \(\Re(z)\), \(\Im(z)\) plane. The gridlines are added with interval unity.

For the testing, no labels are provided.

lines \(\Re(f)= \mathrm{const}\) and
lines \(\Im(f)= \mathrm{const}\) are drawn.

Maps

The map by TORI, generated with routine conto.cin, left and that generated with routine conto01.cin by ChatGPT, right:

Contour lines of integer levels are drawn with thick line.

The nodes of the mesh are intentionally displaced from integer factors of 0.1 in order to see defects of both algorithms in vicinity of zero.

Generators

The generators are supplied at the descriptions of the figures above.

Should they be repeated here?

Should the draft routine conto01.cin be loaded as a separate article?

Observations

The fist version of the version conto01.cin It produces almost the same complex map, as conto.cin.

The main differences:

1. The eps file generated with conto01.cin is 3 times longer than that generated with conto.cin.
This is expected to be improved in the later versions.

2. At the saddle point, the conto01.cin turns the contour line, while conto.cin sometimes succeeds to continue it straight; look at behavior of the dark pink line \(\Im(f)\!=\!0\) at the center of the picture.
This is expected to be improved in the later versions.

3. conto01.cin is expected to be more stable at cells where the value of the function at several grid points coincides with the level of the contour line.
This is rare case, but the stability of new routine in this case still needs to be tested.

4. Using conto01.cin, the color and thickness of the contour line should be specified begore to call function "conto".
Using conto.cin, the the color and thickness of the contour line can be specified attar to call function "conto", and the "stroke" should be added.

Warning

The software discussed is under development and testing.

However, you may use it at your own risk.

At the reuse, attribute the source. It helps to trace misprints, if any.

References

Keywords

«ChatGPT», «Citizendium», «Conto.cin», «Conto01.cin», «ContoTestQuadraticMap»,