Ah, the memories. The ZX-81 was also my first encounter with a computer, my grandfather bought one soon after they first came out. He was a former codebreaker for the Admiralty during WW2, and university professor at Manchester where they had a machine he described as being as large as a room. I still feel particularly sad that he never got to see how modern computing turned out, as he died in 1987.
The one thing that sticks in my mind with the ZX-81 was typing in and running the code for something called "Life", which generated some really interesting (blocky) patterns that evolved over time. It left a huge impression on me, and helped make me into the geek I am today!