Some years ago, to fight off boredom during a long train trip, I coded this small BASIC program for the ZX81, which draws the Sierpiński triangle using the chaos game algorithm.
The program requires an unexpanded 1 KB ZX81 and runs on compatible computers, such as the Lambda 8300, as shown in the below video I recorded today.
You can either see the program in action on the online ZX81 emulator (press the R key followed by Enter (NEW LINE) to run or K key followed by Enter (NEW LINE) to see the BASIC listing), or download the .p file.