Accuracy vs. time
| However, suppose all of z0, ..., z100 lie within a distance of 2 from the origin. |
| Can we conclude the sequence never runs away to infinity? |
| Unfortunately not: maybe z200 will be farther than 2 from the origin. |
| Now we must make a choice. Select some maximum number, N, of iterations we are willing to try. |
| If all of z0, ..., zN lie within a distance of 2 from the origin, we assert the sequence will never run away to infinity and so z0 belongs to Kc. |
| This leaves open the possibility that we incorrectly conclude some points belong to Kc. |
| For example, here are two renderings of Kc (the points painted
black) for the same c. On the left, |
|
| Generally, the larger N, the fewer mistakes we make. On the other hand, the larger N, the more computer time needed to generate the picture. |
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