| The graph of the logistic map is a parabola opening downward, and passing through the points
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| Note the highest point of the graph occurs at
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| L(1/2) = s⋅(1/2)⋅(1 - 1/2) = s/4. |
| For the same reason we wanted to keep the tent map inside the unit square, we keep the logistic map similarly confined. Consequently, the range of s-values is |
| 0 ≤ s ≤ 4. |
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| We shall see that as s changes within this range, the orbit x0, x1 = L(x0), x2 = L(x1), ... undergoes a remarkably rich range of behaviors, some details of which are not yet understood despite years of study by very smart people. |
| This is a sobering lesson in humility for mathematicians: that there is something we do not understand about parabolas. |
Return to the Logistic Map.