This worksheet iterates the function f(x)=rx(1-x).
It plots the graph of the n-th iterate of f on the interval [a,b].
So if n=4, then we plot the graph of f composed with itself 4 times. It also allows plot the graphical representation of iterates of f^n for
the initial condition x0. (The process g is the power f^n.) The first n*n0 iterates of f are taken without plotting, then the nextn1 iterates of f^n are plotted. If n0 or n1 =0 then this is not done.
n iter of f plotted
x0 initial condition
n0 number of iterates of x0 taken by f^n without plotting n1 number of iterates of x0 taken by f^n which are plottedwith(plots):r := 4.0:
n := 3:
n0 := 0:
n1 := 0:
a := 0.0:
b := 1.0:
x0 := 0.1:f := x -> r*x*(1-x):g := proc(x)
local y,i :
y := x:
for i from 1 to n do
y := f(y):
od:
y;
end:pic := {plot(g(x),x=a..b, resolution = 2000,thickness=3,
color=black,tickmarks=[2,3])}:
pic := pic union {plot(x,x=a..b,thickness=3,
color=black,tickmarks=[2,3])}:for i from 1 to n0 do
x1:= g(x0):
x0:=x1:
od:for i from 1 to n1 do
x1:= g(x0):
pic := pic union {plot([[x0,x0],[x0,x1],[x1,x1]], color = blue)}:
x0:=x1:
od:display(pic);