In the pictures, red lines show graphical analysis, while black lines show the axes, the function f(x), and the diagonal line y = x.
| Attracting Fixed Point: 0 on f(x) = x2 | |
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| Nearby point: x0 = -.3 | Nearby point: x0 = .4 |
| Both nearby points are pulled closer to 0, the attracting fixed point. | |
| Repelling Fixed Point: 1 on f(x) = x2 | |
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| Nearby point: x0 = .75 | Nearby point: x0 = 1.25 |
| Both nearby points are push away from 1, the repelling fixed point. | |
| Neutral Fixed Point: 0 on f(x) = x(1 - x) | |
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| Nearby point: x0 = -.3 | Nearby point: x0 = .2 |
| This point is pushed away from 0, the neutral fixed point. | This point is pulled toward 0, the neutral fixed point. |
| The neutral fixed point, 0, is an example of a saddle. That is, it attracts in one direction and repels in another. | |
