Cauchy Integral Experiment

[Kouznetsov]

Well I suppose I could fit it with the Taylor expansion at, say, 0 and 3i, not sure about the asymptotic yet, but that would give good enough plane coverage for the zoom-in.

Yes, these two are sifficient for the zoom-in.

However, I'd probably want to have even more decimals first, at least reproduce the 14 decimal thing, so I'll probably need to go for the Gauss-Legendre process.

You may take the ready-to-use alforithm at CZ,
http://en.citizendium.org/wiki/Legendre-...re_formula

there is an example of the implementation (and test with 32 digits) at
http://en.citizendium.org/wiki/GauLegExample/code

By the way, does your C++ compiler support the complex<long double> variables?
Then, perhaps, you could change to C++;
and in my codes, you may change the definition of z_type to complex<long double>

Or I could use the approximation already given in the paper.

Yes, go ahead. You may plot hundreds of beautiful pics.
You may download also the conto.cin
Ii is designed for plotting of maps of singular and fastly growing functions.

.. what did you think, when you ran that first graph and saw the fractal contained in it?

I thought that God sends me the beautiful flower as sign of her love.

Did it take you by surprise?

Not so much: I saw it in my dream, sleeping, and in the morning I drew it with pensil and colored pens. Then I tried to calculate it. As you, I increased the precision gradually; so, the beauty of the God's gift revealed step by step. But still I do not understand: why the colleagues working on this problem during many generations did not see or did not accept this gift? You see, it is so easy...