A rectangular region of a cellular automaton (CA) pattern is sampled and then used to tile the plane. Not quite finger painting, not quite a kaleidoscope, but great fun nonetheless! Just mouse around in the bottom CA display. The resulting tiling on top is like a bee's compound eye with its many lenses.
There is a lot of variety here. You can vary color, size, and even apply Boolean logic operations between two samples. This Demonstration was created in homage to the computer artist Hillary Kaplan, who exhibited a similar program at the 1986 SIGGRAPH Convention, running on a 8 MHz Mac Plus with 128K of memory—written in assembly language!