Experiments with the Logistic function
| > |
| > | r:=1; |
| > | f:=x->r*x*(1-x); |
| > | plot([f(x),x],x=0..1,y=0..1,color=[red,black]); |
![[Maple Plot]](images/experiments with logistic2.gif)
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | % PERIOD 1 |
| > |
| > |
| > |
| > | r:=2; |
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | % PERIOD 1 |
| > |
| > |
| > |
| > |
| > |
| > | r:=2.5; |
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > |
| > | % PERIOD 1 |
| > |
| > |
| > |
| > | r:=3.2; |
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > |
| > | % PERIOD 2 |
| > |
| > |
| > |
| > | r:=3.5; |
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | % PERIOD 4 |
| > |
| > |
| > |
| > | r:=3.8; |
| > | evalf(f(0.2)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > | evalf(f(%)); |
| > |
| > |
| > | % NO PATTERN |
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