Drawing artifacts are caused by the lost of precision when floating point operations are simulated via 32-bits integers (with just 4 decimal digits in this case).
Precision-wise there is one minor improvement possible, with emphasis on minor
... The "set /A" integer division truncates towards 0 in the sense that 199/100=1 and -199/100=-1. A better 4-decimals emulation would round to the nearest integer, instead. For positive values, this would mean replacing, for example
set /A xSquare=xIter*xIter/one
set /A xSquare=(xIter*xIter+one/2)/one
For values of unknown sign, there would be an additional "if" needed to choose between "+one/2" vs. "-one/2".
I want to post a graphics mode Mandelbrot Set image so you can compare both versions, but when my old Turbo-C program with BGI graphics show the image, it can NOT be copied via Shift-PrtSc key. Anybody knows how can I copy that image?
I doubt many know Borland's BGI nowadays, and those who do may be approaching the memory loss phase of life
Seriously, that's badly outdated, both as an IDE and for language support. GCC or the (free and more Windows-oriented) Visual C++ express edition come to mind.
Back to your actual question, if you have any virtual environment available (such as vmware, virtualpc, virtualbox etc) you could probably run the program full screen inside a virtual machine, and take a screen snapshot from the host. There may be ways to do it directly in the host, without any virtual machine involved, but those may depend on graphics drivers, helper apps, or the phases of the moon.