If your system was purchased new anytime in the last 5 years, the Mandelbrot screensaver is likely to run without issue.
The Mandelbrot screensaver has the following formal system requirements
Windows Vista SP1, Windows 7 SP1, Windows 8 or Windows 8.1
.NET Framework 4.0
This is likely to already be present on your system as it is used by a wide variety of software products. If not, it’s a free download from Microsoft.
512MB of memory (or greater) recommended
The images generated by the Mandelbrot screensaver require a large amount of calculation - and therefore it places a high load on the CPU of your system. I therefore don’t recommend using it on servers (where the high CPU load might interfere with normal operation) or on laptops (where the power drain may be a problem). Of course, you know your situation better - make your own judgment.