This story has implications, for mathematics, for science and engineering, and for education. In mathematics, the use of visualization leads to interesting conjectures, which would never have been contemplated without such technology. Further, as Fatou and Julia discovered, even if you can prove theorems, you often can't communicate why they are interesting without the illustrations provided by computers. The implications for science are probably more important yet. But exploiting the instabilities should lead to the robot moving fluidly, expending far less energy, like an experienced skier floating down the slope, constantly out of balance but with effortless ease.
Computers also allow the use of far more interesting examples, much closer to real problems.