I had a PCjr, which was an 8088. Very slow, EGA graphics. 256k RAM. I did have a 20Mb hard drive, though.
I wanted to verify that algorithm, though. So I bought some books on how to program in C from Waldenbooks. After not too long I managed write a program to draw a Mandelbrot set on my PCjr. It was incredibly slow: I watched it paint each pixel, and let it run for many hours before I would get a complete set. But after much trial and error, it worked.
I was 16 years old. It was the first thing I had ever done that I was really proud of.