Dr. Landelbrot is the inventor of the confusionator, which creates Random Events in the hopes of balancing order against chaos in Neopia. He has had many different laboratories in Neopia, the first being in Moltara's water tower, but currently resides in orbit around Neopia on board the spaceship, the Coincidence.
My Random Event machine is malfunctioning. What, you thought Random Events just happened randomly? Pish tosh! Back in the early days of Moltara, I invented a technology to create chaos. Just as Moltara maintains balance with the fiery magma at its core, so too must we balance order with chaos. I took it upon myself to spawn random events, er, randomly. But I couldn't reach enough of the planet from underground, so I was forced to invent a spaceship. From space, I can cause probability vectors to instantiate virtually anywhere on the planet and its surrounding orbital bodies. I laid in a good supply of Cog Stew and Ionised Onions and have been here ever since. Only -- no doubt due to an aspect of chaos theory I haven't been able to interpret yet -- my Random Event machine has, well, stopped.
Landelbrot is apparently very old, being present in the early days of Neopia at least one thousand years ago. The Coincidence itself has existed for centuries at least.